Accents and the socio-cultural process behind each person's idiolect (their personal way of speaking) are complex and fascinating (sorry English linguistics/dialects is just one of my narrow interests!). I don't think AS is DIRECTLY responsible for your 'lack of an accent' (which of course to anyone outside the US is a very strong American accent, no doubt) but perhaps an indirect result of it.
For instance as someone with AS you might avoid direct socialising with peers in day to day life, and if you listen to alot more TV, movies than you talk to people you're bound to be start being more influenced by it (wittness Australian teens using terms like 'douchebag').
Perhaps if you identify more with intellectuals, you mightly subconsciously strive to adopt the so-called national 'prestige norm'. Maybe your innate prejudices mean that you try to avoid the southern accent because of it's negative connotations.