Depends on the system. Some AWD's will put the power down no problem, spin all 4 wheels and rocket off (Impreza's, Evo's, Skylines and such. Actually, Japanese are good at this shit

). Some other AWD types tend to "bog down" from the line with an agressive launch. Famous case-in-point being the Audi R8, which is kinda weird since their quick versions (S and more notably RS) do not suffer from the same problem. The Quattro system has been prime material for years now, but for some reason in the R8 it doesn't like hard launches.
European car makers in particular don't make AWD systems that are good at hammering a car away from the lights. BMW, Merc, even Porsche. Probably because Europeans make expensive cars driven by all kinds of people (you won't find blonde housewives driving EVO Sti's...), the AWD systems they use are geared very much towards stability, safety, security.
Whereas the Japs put it in "to go faster", hehe.