I would bet not, as the key that closes the F back to the body also opens the cassette. As the F2 has a hinged back, I imagine that there is no mechanism to perform that function. But I'll wait for someone who actually owns an F2 to chime in!
There was a 36-exposure cassette for the F2, it was Nikon model AM-1. Whether these are the same exact cassettes as those for the F, I don't know. However, the F2 does have an open-close key, as you can see in the fifth picture on this page.
the f2 also keys cassettes -- that's why you have to turn that little handle thingy on the bottom to open the back. I sincerely doubt Nikon would have made a different cassette --- backwards compatibility was more popular back then.
Leica did a similar thing -- black knob Leica film cassettes will only work in LTM cameras, but those with chrome knobs were made so they work in both LTM and M.