Of course you can, that's the idea and definition of cross-processing ;-).
Chemistry is not ruined, however there might be SLIGHT differences how much the wrong types of film exhaust the chemistry. That's why the labs have some kind of instruction how much film they can cross-process (something like 20% of their film IIRC) without a need for any adjustment in replenishment ratios etc.
In practice, it shouldn't affect significantly how you can reuse the chemistry, at least if you don't overdo reusing. In any case, if you want to have very repeatable results in C-41 in small tanks, you should use at least the developer as one-shot, even if you do just C-41 films.