I think parents can help you become more functional; they can also be roadblocks in your way. Either way, you've got Asperger's, but they can make the difference (either by neglect, abuse, or overprotection) between being completely independent and needing a lot of help, maybe even a disability check. NT children are similarly affected by parental mismanagement, but not as severely (lots of NTs have issues dating back to abusive or neglectful parents); environment seems to have more of an effect on autistics because we need more help learning and generally are more vulnerable to stress.
So... You'll be autistic whatever anybody does; but your parents can help or hurt you. If they do everything for you; if they constantly belittle you; if they leave you alone and without support; you'll end up having a much harder time adjusting to the non-autistic world than if they're supportive. I guess that's obvious, though.
BTW, even if you do have horrid parents, there's nothing saying you can't catch up later on. I'm doing that right now--five years behind what I could've done, I think; but learning steadily anyhow. After you're about 11 or 12, your parents start having much less of a say in how much you learn and how well you do it; by then, you're mostly making your own decisions, even if you don't have the skills to support yourself yet.