Hey Pratik,
To be honest, I am not too sure and it might very well be the grey zone. I think the best bet is Ayellet. In fact, she was the one who suggested me to apply for PBC when I went to see her the first day. Later on, the head of our group took care of this. As mentioned to me indirectly, there is lot of push and pull that might go on underneath; if not in PBC, then on how it will be accommodated to your existing fellowship. The point is that PBC + your fellowship will likely exceed the 12000 NIS/month limit of student-visa.
Short story: your best bet is to keep Ayellet and the other guy you want to work with, in the loop.
Cheers,
Shashank