Should I tell my advisor that I have an autism spectrum disorder?
As you propose, this has an obvious helpful component.

What's a possible down-side? Well, medical/personal issues are protected information (thinking about the U.S., at least), and in most situations anyone else in whom you've confided is not allowed to disclose anything about it to anyone else. We can see the sense in this. However, it does sometimes create a burden and/or awkwardness, insofar as the people in whom you've confided are prohibited from using what they know to explain any questionable actions on your part to anyone else...

The operational point, then, is to pay attention to any close interactions with people outside your immediate group, in whom you've confided, that might generate a need for explanation.