The Glock 22 is a full size firearm. It's the same frame as the Glock 17. There's not doubt you can carry it in a good holster, but IMO, it's not a comfortable CCW gun. The Glock 19/23 is much easier to conceal and the Glock 26/27 is the easiest of the Glocks to conceal.
I don't like to carry my firearms in a fanny pack or bag, so someone else may be able to chime in.