Aioli mousse?

I guess it depends on exactly what texture you are trying to achieve. You can make aioli with just egg whites. Serious Eats has a recipe for a yolk free mayonnaise, and you could easily flavor that with garlic. Lebanese Toum is another idea- that skips eggs completely, and you get a really intensely garlic flavored sauce. If you go that route, you can alter the final texture by adding in more oil, water or lemon juice to adjust thickness. Or you could make a traditional version of aioli, and fold in unsweetened whipped cream that has been stabilized with something like instant Clear Jel. Just folding in whipped egg whites would get you a lighter more meringue-like product at first, but I suspect the weight of the aioli would force the air out fairly fast. And it might just taste like a more garlicky raw meringue as well. It's not just about getting air in to make things foamy, it's as important to figure out a way to keep the air in it. Egg whites work best when they get cooked to set the protein mesh, and don't do so well if not cooked. Whipped cream will hold air a bit longer, but without the gelatin to add structure- even that fails after a day. How much stabilizer you will need depends on if you want this mousse to hold shape, or hold up more than a few hours, or just be kind of foamy for a short time.

Probably yes, fold into whipped egg whites (or some use whipped cream), if you already have aioli.
If you're starting from scratch, think about various recipes for garlic mousse or dip.
https://www.google.com/search?q=garlic+mousse&oq=garlic+mousse&aqs=chrome..69i57j0l5.2144j0j7&sourceid=chrome&ie=UTF-8
But then, aioli is already (almost) that.