Yes, you can. I have rigged a Petzl Ascension ascender in between my harness and a webbing runner as a chest harness on a fixed top rope.
Yes, I have taken a fall and it held. I have talked to one guy who fell and the ascender torqued off the rope; so, it can happen. There is inherent risk since there is no backup to this system. It's all risk assessment, right?
Greg