I'll tell you right now, and I have removed thousands of broken screw, broken easy-outs, and broken carbide drills........If you do not have a rigid setup, carbide will bounce off of carbide. You can try it, but it you break the ball off in there, you may just be doublefucked. If it were me, I would make a strap that takes in both holes either side of the broken bolt. Only on very rare occasions do you ever use a small carbide drill bit in a hand drill. If you wiggle once, and the drill is in there by any depth at all, you will snap it off every time.
Give it a try, the worst that can happen is you screw it up more. If you can see the bolt and the drill bit, weld a nut over both of them. The weld won't stick to the aluminum. You stand a better chance going that route that you will trying to drill it. You might also want to try a pointed punch and shatter the carbide bit. If it is down in the hole, get a punch that will fit in behind it, and give it hell. Then get a small pick and pick out the pieces.
IF per chance you get the broken carbide out, get a little larger HSS bit, and drill a little larger hole so you can tap the bolt but stay inside of your current threads. Tap it with a L.H. tap. The get a L.H. Socket heat cap screw, or a bolt, and screw it down into your current bolt. Use a Grade 8 or a S.H.C.S. as they are a little tougher. When you replace the bolts, get a good stainless bolt, or us some socked head cap screws as they have a black oxide coating and will not corrode in the aluminum.