Unlikely. There are many orders of magnitude more ways to be well adapted to one environment than to be adapted to two or more environments. So if an organism is well adapted to high radiation it’s probably terrible at many, many other things that are irrelevant where it is now. There are plenty of extremophiles apart from these radiophiles. You don’t see microorganisms adapted to very high levels of acid, pressure, heat, cold or anything else suddenly exploding into new ecological niches regularly.

Consider the analogy to multiply resistant to antibiotics bacteria. They’re far more common in hospitals than elsewhere because hospitals are swimming in antibiotics. Once they leave the hospital environment they’re paying a cost to be antibiotic resistant with far lower benefits so they either lose the capacity or are outcompeted by other organisms in the same niche.

The explosion into a new niche does happen occasionally, when a new capacity is extremely useful or when an adaptation is discovered that is far more efficient but has similar costs or better than the alternative. I’m not familiar with any examples in microbiology but invasive species exist and so do we so we have existence proofs in macroorganisms.

In general organisms create bad consequences when they're too adapted to Earth and reproduce excessivly in some way. If they die out because they're adapted to space instead of Earth that won't be a problem for us, though it will be for the organism.

Since Earth is very different from Space, they would be badly adapted to Earth.

So there is very little to worry about from alien world infections.

And also, incidentally, why most awful diseases come from Africa, and very few from the Americas.

This was my first thought as well. Although that adaptation wouldn't be much of an advantage anymore once the organism got back down here. Or would it...