Nah they usually come in as a youth player anywhere between 16 and 20 under a different name. Some regens are easy to spot, especially if its someone like a Totti, Zidane etc, their stats at 18 are usually already superstar like.
To find them, most of the time they should be in the under21 team of their nationality, so try looking there if you want some.
No they dont start at the same team they came through the youth system with.
I used to have a regen finder program and Zidane's regen came up through the Liverpool youth, Robben's at Ajax, Kluiverts came up through PSV, van der Vaart's regen didnt come up through the ranks with any team, he was available a-la Taribo West style.
So as you can tell, its pretty random.
Although i must admit some do come in at a later age, on my game, Hyypias, Nedved, Smicers and more than likely a few others regen came in at the age of around 27/28.
Do i buy them? Yeah, if i feel its a position in my team i feel needs strengthening. Why not?