Immortality (we have always been talking about the "inconsequential" one) wouldn't make the universe teem with life, because it wouldn't grant us the ability to live on other planets or to travel fast enough to reach other solar systems. Mind that the fact that you don't age doesn't mean that you wouldn't want to go on a trip that lasts a million years and that you could get enough food on that spaceship for that trip or that you reach a planet within ITS lifetime!
Also, reproduction does have a limit. If you don't age, you can still starve to death. So the food, or rather the energy on Earth effectively limits the number of individuals that can live on Earth.
EDIT:
I still believe the idea of immortality is silliness, and I just thought of a good reason why:
As it happens, there is a certain type of jellyfish that is potentially biologically immortal, as it can reverse its life cycle by transforming back into a polyp, thus escaping death. These jellyfish are not much more common than any other creature on earth, however, as they are extremely vulnerable to predators in the polyp stage and they are still vulnerable to disease as well.
But, if we somehow able to create a biologically immortal human mutant by stealing genes from this jellyfish, we would have, for all intents and purposes, a biologically immortal man.
I didn't check if that thing with the jellyfishes is true, but you just contradicted yourself.
