Most of the systems use a 3" duct, some use 4" and some even larger. So, to direct it through a 2" hole would not be a good idea. You also want that penetration to have some kind of termination to prevent rain/snow/etc. from coming down the pipe and dripping into the room. You should not normally combine this output with anything else (like a sewer vent), either. You may be able to enlarge the opening, depending on what it is currently used for to accommodate the (new?) use.