It can't hurt to try, but depending on how thorough the exam is, I'd have to say you don't stand greater than 50/50 chances of (barely) passing a test that's almost half and half calc 2 and 3. The comments that you cant neglect calc for your career are true, but it wont actualy come back to bite you in the bellybutton if you carry the momentum you take into the test and 'finish' studying these topics over the next 3-6 months.
Go for it, but don't bet anything important on it.. For the physics class, if you really are serious about it and not just trying to find shortcuts, you can probably get by with just passing or knowing Calc 1, and taking calc 2 at the same time as the first physics class. You'd most likely have to talk to the teacher and effortlessly show him you've done the homework and deserve in. If you can truly integrate (no pun) the conceptual understanding of Calc1 and know it and everything it implies like the back of your hand, youve done the hard part.. Calc2 is more of the same IMO. Diff EQ isnt that hard at all once you've waded thru the conceptual obstacles in the calc classes.
I say go for it.. You cant push back your limits till you find em. IMO youll be a lot better off trying it, even if you fail the exam itself.