I don't see any reason it wouldn't work. I'd use a magnum primer, and verify the bore is clear before making another shot. I would also check the size with a set of calipers; I say that since I don't know the dia. of .22 cal air rifle pellets. Case size is a little critical, What I mean by that is that the .22 Hornet would probable work great, while the .220 Swift would have too much case capacity to make efficent work of it.
You might expermint a bit and get back to us, I'm curious to see the results. I doubt that it would make a good varmint gun, even if the varmint of choice was field mice, I just don't think you'll get the velocity you want. Informal shooting in the basement is a whole different matter, for that I think it will work well. Let us know.