This is an odd one. I have been called up in previous versions of MLB the Show in September, only got a few at-bats, then made the MLB team in the next year. I should have been eligible for Rookie of the Year, but wasn't according to MLB the Show (not sure if that was a bug that has been fixed). According to MLB, the limit is 130 AB's or 50 IP.
I was called up in late July this year, and my stats were good enough to beat out others for ROY.