No. I've yet to see higher end EA games available through Steam activation. However, that's mostly because EA has its own online activation system that makes your game available through the EADM. I've done this a couple of times myself, actually. Works brilliant. As for Steam in-game overlay, you can just add the game as a shortcut on Steam and by doing that, Steam in-game overlay will be available for that game.
Thanks
Iceman