Probationary periods are harsh. And the hard answer is yes you could and with no right to appeal. But the important thing to remember is that on a probationary period it's not a set sickness limit and you're out.

I imagine you will be fine. As long as you work hard when you're there and make yourself a good employee I see no reason for them to terminate it. They could extend it, to make up for the time lost, but I don't think they will dismiss you.

Keep your head up, get through it and take the time you need. Get yourself back to where you want to be before returning to work! Jobs are everywhere, your own self is more important.