It would be up to the discretion of the event host whether or not it would be allowed.
Personally, I think it would be hilarious.
That said, how does a sentry gun know to stop firing on whatever target it is engaging? If the sentry was equipped with a full power AEG it could do some serious overshooting if its target didn't move out of the line of fire. Obviously, human players can tell when their target is hit and will stop firing; this isn't true of a sentry and that is a problem.