Okay, first, we know now that comet Sliding Spring is going to miss Mars, by about 10 Mars diameters (though some of the surrounding particles will hit Mars of course). C/2013 A1 But it's interesting as a theoretical question for future comets.
It depends where it hits. If it hit one of the polar caps of Mars - it could create a liquid lake beneath the cap. I'll need to look up the figures here, I think I've seen a paper about it somewhere. But if you have a big enough impact - it can create a lake that stays liquid for a surprisingly long period of time.
We are talking about periods like a thousand years here. It gets covered over by a layer of ice quickly, which also acts as insulation which holds in the heat - a bit like the way an igloo keeps Eskimoes warm.
And liquid water can retain a huge amount of heat - has a lot of thermal inertia - and needs to give up large amounts also to turn to ice. Also - a thin layer of ice will act as a greenhouse keeping the water beneath it warm by the solid state greenhouse effect.
So - this probably happens on Mars from time to time, providing temporary habitats where life can flourish. And especially if life is already there in a low level way all the time - then this may be the occasion that causes some lifeforms to grow rapidly and flourish for the thousand years or so the lake lasts for.
So could happen. And we might also find evidence of previous impacts on Mars that created lakes similarly.
Most of this is from a paper I read some time back. But I can't remember the title or where I read it. So will try a search and see if I can find it and if so update this answer with the reference and more details.
As for other parts of Mars - to let loose a flood - probably has to be high lattitudes - though there may be some ice even at equatorial regions just below the surface - trapped ice - detected (tentatively) from orbit by radar.
So - if it hit just the right place I suppose it could cause a flood.
But - the water would soon evaporate in the warmer areas of Mars. So - I think best place to have long term effects is in the polar regions. There - far more water to melt, as you say the impact releases a huge amount of heat - so - if you also have enough ice to melt...
EFFECT OF A BILLION MEGATONS ON ICE
Water needs 333.55 kJ/kg. A billion megatons is 4.184e+21 kJ. So at 333.55 kj / kg, that's enough to melt 1.2543846e+19 kg of ice to water. Or 1.2543846e+16 tons. Or same number of cubic meters (for metric tons) so in cubic kilometers, I make it about 12 billion cubic kilometers.
Can that be right?
Surface of Mars 144,798,500 km^2. So looks like you are talking about enough heat here to recreate the Mars ocean again.
Can this be right?
Of course a lot of the heat would be dissipated - still - if he is right and it is a billion megatons...
If this is right - I imagine the main limitation then would be the diameter of the crater. So suppose the crater is 100 km in diameter. And excavated to 1 km deep (I will need to look those figures up also). Then that's a maximum of 30,000 cubic kilometers of ice - but much of that excavated rock rather than ice.
Seems more likely that 12 billion cubic kilometers anyway.
EFFECT ON MARS ATMOSPHERE
Mass of the Mars atmosphere is ~2.5 x 10^16 kg Mars Fact Sheet And that gives atmospheric pressure of 1% of Earth normal at the deepest points like Hellas basin.
Dry ice needs 571 kJ/kg enthalpy of sublimation Dry ice
So - to get to say 10% of Earth's atmosphere as sublimated CO2, if it is a direct hit on dry ice, then 2.5 x 10^17 kg would need 1.5*10^20 kJ.
1.5e+20 kJ is the equivalent of 35,000,000 megatons.
So if he is right and it is a billion megatons (I haven't checked his calculation) - that's enough to evaporate dry ice enough to create not just a tenth of Earth atmosphere, but the whole of it, 100%, three times over.
But that is - if the dry ice is available on Mars to be evaporated and if you get a direct hit, and not taking account of the need to heat the dry ice up before evaporating it .
And of course - much of the energy is used to create the crater and excavate the debris and send that into orbit. And much will be absorbed by underlying rock. So how much would be able to evaporate the dry ice?
Seems the earlier 30,000 cubic kilometers is a better upper bound here also.
In that case, with each cubic kilometer - similar to ice, about a billion tons (1.6 billion tons for dry ice but similar), you are talking about 3*10^13 tons so - way short of enough to make even a slight change in the atmosphere of Mars.
The melted lake seems a more likely scenario.
But - I'll see if I can find some papers on all this.
RELEVANCE TO PRESENT DAY MARS LIFE AND PAST MARS LIFE
I'm interested in this because of its relevance to present day indigenous Mars life and as a possible way to recreate and study an event that happens only rarely in the Mars geological history.
As you'll see from my other answers, I'm no fan of terraforming - not right now anyway.
The problem with terraforming is that it is temporary - and we are doing it for our descendants a 1000 years from now - and - we just don't know enough yet to know what the effects would be - or what they would want.
And also needs continuous high technology civilization to continue for a thousand years - or could make Mars worse than it is now. I see no point at all in a few decades attempt at terraforming Mars which is then cut for reasons of budget and fails.
And - postpone it by a century and you might find a way to trim 500 years off the process. Or might decide - that it is not worth doing or is some better thing to do.
Because it is irreversible - once you introduce life to Mars then you can't remove it again.
And Mars is so different from Earth it needs its own solutions - and we don't understand clearly how Earth works - but know for sure - that if you put Earth in Mars orbit - then its oceans would freeze over and it would not stay terraformed for long at all.
If we want to experiment with things like that - far better to use a Stanford Torus or similar. Costs far less. Is self contained. Can finish it in a few decades. Can reconfigure with any level of gravity or temperatures, sun / night cycles etc etc. If something goes wrong, start again with new parameters.
And enough material in the asteroid belt to make Stanford Torus habitats with 1000 times surface area of Mars.