It seems to me you're asking about cherry desserts that fit in a graham cracker crust, rather than a cobbler. For most of us, there are two kinds of cobbler crusts. One is made from a batter, and the other is pretty much a generic pie crust. Graham cracker just isn't part of the "cobbler" concept in most of the U.S.
When you talk about graham-cracker cheesecake crusts, you're talking about a "pressed-crumb" bottom crust, which isn't a cobbler. This type of crust is most either used to hold some kind of custard (like cheesecake), or is blind baked and filled with something that doesn't need much or any subsequent baking.
A cheesecake base with a deep cherry topping is one great idea. Considering you brought it up, it's probably what you were thinking all along.
The problem with using a straight cherry "filling" is getting it firm enough to hold its shape when sliced. No doubt there are ways to do this, but I don't know what they are. At any rate, it's not unusual to make (or buy) cherry pie filling (cherries, water, sugar, corn-starch), and fill a graham-cracker pie crust with it. It's even got a name: "Cherry Crisp Pie."
Along the top-crust line you can use graham crackers to make a "crumble" or "crisp" top crust. And bake, or simply clump along the top of cherry pie filling. Maybe you meant a crumble or crisp when you said cobbler -- the only thing different is the type of crust.
Hope this helps,