If humans became immortal for repeatedly having sex we would quickly exceed the planet's ability to support us, and we're already reaching that limit with just being mere mortals.
It's really hard to make any predictions about how immortality would affect the planet's ecosystem. For starters, with more advanced technology the planet can probably support a trillion people. We would have to generate power via fusion and use it to grow our food in huge vertical farms. And we would have to live vertically as well since there is only so much land we can appropriate for our uses. Consider that one trillion people at the average population density of Manhattan (~70,000 per square mile) would occupy perhaps 15 million square miles. This still leaves 42 million square miles of land for nature. So it is at least possible to support many times the number of people we have.
But let us consider how immortality might affect us. What is the usual reason people give for having offspring? Generally it's so that a part of them survives after they're gone. In a world where lifespans are indeterminant that reason suddenly vanishes. My guess is many or most would choose to not reproduce should they have the option of immortality. Or you could legislate this if need be (i.e. perhaps render the person sterile should they choose immortality). Regardless, I'd say even without coercive methods the population wouldn't explode if immortality became a reality. Most of the reasons for having children vanish in a world where lifespans are not biologically determined.
Finally, it must be noted that immortality in the strictest sense can never happen. At best we'll have indeterminant lifespans where you won't age or die of natural causes, but can still die by external means. I think I remember reading that based on current statistics on causes of death, perhaps 50% of the population would die before their 1000th birthday. Few would live to 10,000. We would probably become more risk averse and make things much safer in such a world. Even so, I highly doubt you could get average lifespans much over 100,000 years. Sooner or later the odds of something beyond man's control, like a natural disaster or asteroid, will catch up with you. Maybe you'll get a few eccentrics living to 10 million years by never venturing outside their bunker, but is that really living?
Althoug I do feel younger!
