I would imagine it wouldn't have been unheard of, but it is really a question of which CS regiment vs. which Federal regiment. I don't have any numbers handy right now, but the Army of the Potomac was using just as many, if not more, arms other than the M1861 during the spring '62 campaign so any other type of arm would theoretically be just as appropriate in the general realm of things. Production of the M1861 didn't catch up with demand until the early summer of 1863.
Hopefully someone can add to that.
Cheers,
Garrett