Not directly. But apparently, if it exists, it helps explain the Scattered Disk population.  This is a population of large objects that criss-cross the Kepler belt in very elliptical orbits and at their closest reach in to just beyond Neptune.

Then Neptune would divert some of them to Jupiter which would then divert some of those to Earth.

This is a link to the paper here: EVIDENCE FOR A DISTANT GIANT PLANET IN THE SOLAR SYSTEM, see their section 5. Scattered disk.

Please note though, it does not mean that we will suddenly start to get Sedna sized objects hitting Earth :).

We already know about the scattered disk. If we find that Planet 9 exists, nothing changes except we have a better idea how the scattered disk came to be the way it is.

These objects are not in orbits that go through the inner solar system. It would take a lot of delta v to do that and Planet X couldn't do that by itself.

Just as it would be impossible for Earth to send an asteroid in to the inner solar system inside of Mercury, almost impossible anyway. But Earth, over thousands of years and many flybys, could help send an asteroid to Venus, then Venus could eventually send it to Mercury and Mercury then could send it into the region between it and the sun, and turn it into a "vulcanoid" if they exist - asteroids orbiting between Mercury and the Sun.

So, in the same way, Planet X would help disturb these scattered disk objects from beyond Neptune into sufficiently elliptical orbits so they get within the reach of Neptune.

Neptune would then perturb them into orbits that take them within reach of Jupiter and Jupiter then brings them into the inner solar system. At least in the majority of cases, would be like that, if I understand this right.

The whole process would take many thousands of years. It's not like Planet X would lob an asteroid towards Earth and next year, or century, it arrives here.

Apart from anything else they would also be at widely varying inclinations and to have a reasonable chance of hitting Earth, have to be perturbed into the plane of the Earth's orbit by Jupiter to have a decent chance - or pretty close to it.

During this process, then there would be both big and small things sent into the inner solar system. But anything really big gets broken up by Jupiter into smaller pieces, maximum of 10 kilometers or so in diameter. That's through tidal disruption as they pass close to the giant planet.

Large objects can't hold themselves together under gravity when disrupted by the tidal effects of a close flyby of Jupiter -  and get torn apart. The intermolecular forces that keep rocks together can only resist gravity if the object is small. We saw this with comet Shoemaker-Levy which broke up into lots of smaller comets because it was too large to resist the tidal effects of Jjupiter.

Comet Shoemaker–Levy 9 broke into lots of smaller pieces due to tidal disruption passing close to Jupiter. Big objects coming in from the outer solar system would get disrupted by the gravitational field of Jupiter in the same way at one or other of their frequent fly throughs of the inner solar system, and from the cratering record, as well as models, this happens before they can get into orbits that threaten the Earth, Mars, Mercury etc.

Much of it gets ejected from the solar system, hits Jupiter eventually or hits the sun, far larger targets than Earth. But some of what's left ends up on Earth crossing orbits. And all of those eventually get swept up within twenty million years - but not just by the Earth. Even once they become NEOs, they can then end up hitting any of the terrestrial planets, or their moons, or Jupiter, or the Sun or ejected from the solar system. But once they are in the inner solar system, in Earth crossing orbits, the clock is ticking. Within about 20 million years they are all gone, to be resupplied by more.

So - yes seems that Planet X does have a part to play in this process, if it exists that is. But it's like a bucket chain putting out a fire - it is just one of many links in the chain.

We know that it does not send intact Sedna sized objects into the inner solar system from the cratering record. There are no impact craters in the last 3 billion years throughout the inner solar system.

We can see that also from the meteorite crater record of the solar system.

There are no huge craters in the inner solar system younger than 3 billion years, out to Mars.

The Moon, Mercury, and Mars all have huge craters, but the youngest ones date from the late heavy bombardment between 3.8 and 3.5 billion years ago.

Craters on Mars

Impact from 3.8 billion years ago when large asteroid impacts were still common. 3D map of Mars - Hellas Basin on Mars

Craters on the Moon

The Aitken basin at the lunar South pole. It's believed to be over 3.8 billion years but the exact date is hard to pin down. Impact of an asteroid perhaps 170 km in diameter.

Craters on Mercury

The Caloris basin on Mercury.

Craters on Earth

Earth surely had impacts this large back then as well, but the evidence is probably long erased by continental drift.

The largest crater on the Earth may be the Vredefort Impact Structure in South Africa - this was about 300 km in diameter, when formed. The Sudbury basin is nearly as large, and there are three others in the 100 - 300 km range. See Largest craters ordered by size. These are thought to be the result of impactors of up to 10 or 15 km in diameter.

For the largest I can find, see this Impact of 23-mile-wide asteroid boiled Earth's oceans 3.26 billion years ago (and another link, and scientific paper). When it says it boiled the oceans there - doesn't mean it boiled them dry, just surface layers, and it would come nowhere near making all life extinct.

Even though the "late heavy bombardment" was over, there was a tail-end of not quite such huge impacts that continued, perhaps for another 700 million years. Ancient Asteroids Kept Pelting Earth in a "Late-Late" Heavy Bombardment, up to 2.5 billion years ago.

Craters on Venus

It's largest crater, Mead crater, is 280 km in diameter

Meade crater - the largest crater on Venus, comparable in size to the larger craters on Earth.

As you can see none of the planets or moons in the inner solar system has been hit by a Sedna sized impactor or even a 100 kilometer diameter impactor for over three billion years. It's true that for Venus we have only a few hundred million years of history - but no reason to suppose its cratering record is any different from the others.

It was a significant risk in the early solar system, but not any more.

The reason seems to be due to the influence of Jupiter. As you can see in this diagram it has a Hill Sphere - sphere of gravitational influence - that's nearly a couple of orders of magnitude larger than the Hill sphere of the terrestrial planets.

Hill sphere of the planets (log plot)

So any dwarf planet that gets deflected towards the inner solar system will be influenced by the Hill sphere of Jupiter within a few orbits, and the leading theory for why we have no large impact craters in the inner solar system is that Jupiter defends us by breaking them up, or sending them into the sun or sending them out of the solar system.

It also catches many of the smaller kilometer scaled ones and removes those threats directly. Jupiter gets hit by an object between 0.5 and 1 kilometer in diameter every decade.

The whole scenario gets played out over thousands of years, see  Giant Comets and Mass Extinctions of life.

There are objects such as Chiron that have the potential to do this, but none of them show any signs of doing the first stage of getting broken up by Jupiter quite yet.

It may indeed happen, but you are talking about thousands of years from now. And yes, indirectly, thousands of years earlier, some of those comets may have got to Jupiter via Neptune and previously via planet X if this theory is correct that Planet X helps explain the scattered disk of comets.

But I think it's important to keep in mind that that's a very different thing from saying that this Planet X would be a threat for Earth.

For more about this, see Why This New "Planet X" Is No Threat To Earth :).

And for the truth about asteroid impacts - see my Giant Asteroid Headed Your Way? - How We Can Detect And Deflect Them article - the bit above about impact craters is an extract from there.