Unfortunately the officers at the Amt have large discretionary powers, and it is difficult to answer your question with certainty.
In principle, the only potential point of conflict would be where you have to "demonstrate financial independence" and ability to earn a livelihood. Nothing beats an unlimited work contract at that, of course after the probation. I have been refused PR when I applied with 6 months remaining on my contract at onceone location, but got approved at another location. So you see, it is best to ask your local Amt how they deal with these things there.
Practical advice: apply anyway. It is not that they process the application within a week. In my case they took 2-3 months, plus getting appointment already takes 2-3 months from place to place.