That would actually be very interesting to see, an earth- or firebender as an Air Acolyte. I don't think it was ever shown or stated that any of the Air Acolytes, prior to Harmonic Convergence, were actually benders. However, I don't see why they wouldn't allow benders to join. Espicially since the entire idea behind the Air Acolytes is that they choose to follow the culture and ideology of the Air Nomads, regardless of their actual heritage. The only downside that I could see is the fact that, often times, a person's bending is greatly entwined to their heritage, so that probably leads to a lot of potential recruits deciding to pass it up or even leave later on.
I don't recall it ever being stated that the Air Acolytes had to be nonbenders, so I guess it is possible. One thing I would add similar to General442's response is that the philosophy of the other bending abilities might run counter to the beliefs of the Air Acolytes, which would then make it difficult for them to join. Earthbending, for example, is about facing attacks head on whereas the Air Nomads and Acolytes practice non-confrontation.