Really high functioning autistic people can. Others might need a little extra support, and moderate to severe or profound autism diagnoses can’t. The worse the autism function level, the more likely the young adult will have to live at home or in a sheltered apartment or group home setting. So the answer here is, yes, and no.
Those with just a mild to moderate level of functioning may be able to learn to do many things for themselves and eventually live on their own with limited support. Only the extremely mild to mild cases can live on their own completely without any support at all, although they might need constant emotional support and connections to friends and family. Severe and profound may learn a few new self help skills in their lifetime, but not enough to live entirely on their own.
For those that can’t live on their own, there are many support programs and non-profit organizations that seek to help them live in the least restrictive environment as possible while maintaining their level of personal safety. Some local, state and county programs can also be of assistance with finding residence programs for the severe to profound adults with autism.