Can I bake a "no bake" cheesecake?
I can't say I've browsed through dozens and dozens of no-bake cheesecake recipes but the ones I've looked relied on the ingredients being whipped (usually cream) or gelatin to maintain their shape. Mousse style no-bake cheesecakes use a whipped mixture of gelatin and some milk product that gives the foamy texture.

All no-bake cheesecake recipes (that I've read) require them to be refrigerated before serving. A no-bake cheesecake made with whipped cream, cream cheese, sugar and other ingredients would simply melt into a mess if baked. Ditto for one made with gelatin. 

Baked cheesecakes call for eggs and flour to provide structural strength to hold the fats together. I guess if you wanted to add flour and eggs to a no-bake recipe, it might hold some sort of shape. Or not and you get a less spread out mess instead. I really don't think it's at all plausible and I wouldn't want to test it and clean the mess each time.