The key to fast pop growth is 100% morale, you get double growth when morale is maxxed. I found the +pop growth abilites to be a waste of time, there is an in-game cap on the max pop you can grow per turn (200 million), and +pop growth abilites and tech doesn't raise that. And since you can (and will) hit +200 million with +0 enhancements with 100% morale, and since if you don't have 100% morale you'll only grow for a few turns anyway before hitting 50% and growth stops, my conclusion is that +pop growth is of extremely limited use.
I'd like it to be changed so that the ceiling for growth rises by the bonus to pop growth you have. So a player with +50% pop growth bonus could grow a maximum of 300 million people per turn. This would make the ability useful for the entire game under all conditions (except low morale).
And yes, the computer grows its population extremely well. Better than I can, that's a fact.