In this mythical "no civil war" we're imagining, yes, I think it's likely that one of them would lead campaigns in Parthia - but Pompey rather than Caesar? Pompey would WANT to, of course. But it would have been 15 or so years since Pompey last led men into battle, and in the meantime, Caesar had become the Gallic star. Perhaps we would have had a civil war over THAT issue. Or maybe - one would let the other take armies to Parthia, stay behind, and stab his rival in the back politically!