Having been around this a lot in my life, my answer would be it is totally dependent on the individual. As jpetersonmn mentioned, people with Autism in general have a wide range of abilities and those with Aspergers can vary significantly from very mild to fairly significant.

From my experiences, usually they are amazing people and extremely intelligent and have some abilities I really admire. Of course, many times social interactions can be tough for them, reading body language, facial expressions etc are also not usually something they excel at naturally. However depending on their severity level, most can be taught to do things that come natural to those of us without Aspergers. A friends son with Aspergers has learned to read facial expressions better, but it took him quite a bit of effort to learn to do it fast enough so that conversations run fairly smoothly. But I'd never rule him out from doing whatever he wanted.

While I have no personal knowledge of someone with Aspergers running a startup, I would say that absolutely they could run their own business and excel. But it would all depend on the severity of their condition and their support network.