Depending on the game in question, the game won't work. Some games will work and some will be impossible to play fully even if they could run. The dualshock 4 works on the system and the touch pad just emulates the vita touch screen (So does the dual shock 3, is done with analog clicks)
Games like uncharted golden abyss which has a part that requires you to hold the vita up to a light source, is impossible to do on the PSTV, therefor can't be completed on the system alone. Other games like Ninja gaiden sigma, YS memories of Celsestia or tales of heart R have touch screen functions and still work on the system.
Most of the time if you check psn for the game in question, you can find details if it supports vita tv or not. If you are browsing on the system itself, it won't display games that are not compatible. Here is a link to all compatible games on the pstv.
http://www.pushsquare.com/forums/ps_vita/a_master_list_of_games_that_are_compatible_with_pstv