The answer to the original question is yes.
There are conditions under which a vehicle will pull to one side even after an alignment.
1. Assuming a cheap job where toe was set and maybe even camber, caster could still be off a lot.
2. Even if everything was set properly, and even if your tires are fine...
a. uneven weight distribution or spring pressures could make it pull
b. any sort of binding of a bushing could make it pull
c. a bent or otherwise preloaded sway-bar could make it pull
d. etc., etc., etc.
3. Depending on the alignment job included, and depending on your REAR suspension configuration, there are some things in the back end that could make it pull also.
2006 McLareghini Bugatterrari, Storm Titanium... installed: air horn, Scroth 4-point ASM harnesses, Sector111 halon extinguisher and mounting bracket, Von Hep exhaust and rear panel delete, Pagid brake pads, red Volks CE28n wheels, Toyo RA-1 tires, Nitron SA coilovers, Sector111 (WorksBell) quick-disconnect steering wheel kit. awaiting installation: Scroth "pull-up" lap belts, Sector111 RTD Brace, Tony's heater bypass mod, and dropped steering rack mounting plates.