I think the pass rate for BOTP is higher than the pass rate for IAP. I didn't have to do IAP so I am unsure about it, but only 2 people out of 42 candidates failed the BOTP I was on. Neither was about physical fitness.
I wouldn't stress out about the fitness part, unless you can't even run a km. If you have a few weeks before you go on course, then start working on it. The important thing to remember is that determination is most important. If you are doing a run with the course and you start to fall back, keep at it. Don't stop and walk, unless you are seriously going to die. You also get at least two kicks at the cat in regards to the PT test, so you have plenty of time to improve your fitness level. But start NOW.