Yes, she did become part of the Lifestream. That's what returning to the planet means. You become part of the Lifestream, and the Lifestream is used to create new life. It's always changing.
What I'm unsure of, currently, is about the souls. When Bugenhagen talks about returning to the planet, he's using two different examples. Obviously, a body doesnt stay in the Lifestream, but does a soul? Does it transcend to another plane? Does it get reborn? Or does it float around in the Lifestream? And how could any of those help either Zack or Cloud get to Aerith?