Maybe some day. But we just don't know enough about what could happen. I think it is partly based on an idea that "nature knows best" that if you just seed a planet with lifeforms - that it will automatically come to the very best possible endstate - and doesn't matter what you seed it with particularly.
But - all we know is that it worked on the Earth. But - was it just chance that it survived through the snowball phase? And would seeding ancient Earth with any microbe from present day Earth have achieved the same result? Or would the outcome depend on your choice? If so which are the best ones to use?
With only one planet to go on so far, we can't even begin to start to answer questions like this.
In our own solar system - Mars would be maybe the best candidate - except - that it may well have life of its own there already. Which - hasn't automatically made it into a planet like Earth obviously - not surprisingly as it is so much further from the sun, has no continental drift, and is in a permanent "snowball" phase but also a very dry "snowball" with almost no ice on the surface.
There probably isn't too much that life could do to fix that. On Earth - then the similar snowball phase ended not through actions of life - but because of CO2 from ancient limestone returned to the atmosphere by volcanoes.
Mars can't do that because it doesn't have continental drift to subduct limestone below continental shelves.
We also don't know how easy it is for life to evolve. It might be very hard. But it might also be so easy - that any planet that is moderately habitable already has life on it.
If so - our introduced life - with a fundamentally different biochemistry surely - would either make it extinct, or go extinct itself, or set up some mixed biosphere of some of each.
Are any of those good outcomes? Again - we just don't know enough yet to answer.
And don't know how often natural panspermia happens - and whether it is a good thing or not, whether it might sometimes cause havoc with a planet which has life already - really - we need to know a whole lot more about the galaxy before we can answer this question.