Yes you can fly other A/C in Allied Force, Go into your <Drive>\Lead Pursuit\Battlefield Operations\Campaign\(which ever Campaign you are flying)
Find the "validAC.bin" file & delete it or rename it (I renamed it to "validAC.bin.bak")
Fire up the game & now all bases are visable & you can jump to the base with the plane you want to fly. Some of them don't have skins though which makes them appear all white...yuk. There are tools to fix this but it is time consuming & you should really know what your doing before attempting.
The F-22 Raptor DOES have textures & is a great performer.