I got both Buster Posey and Felix Hernandez very early on. I also got JD Martinez after those 2 and his stats went up after the update. Those are my only 5 star guys, and I got them all in the first couple weeks of playing.
No, the only thing you can do is go into gameplan and have a different lineup against righties or lefties. The game decides what it thinks is your best batting order.