God knows why I dreamt about this. Anyway, I was on the Enterprise with the DS9 crew for some reason, when the Enterprise was being blown up.
Bashir and Dax (Jadzia, even in my dreams, I know who the real Dax is) came down to me, I was sleeping in a shuttlecraft for the benefit of the additional shields.
In theory, would that work? As a second line of defence if the main ship was being attacked?
Meaning you were inside the Enterprise's shields and also inside the shuttle's shields? It might seem like extra protection but the problem I see is that all your attacker would really have to do is get through the Enterprise's shields. If it gets destroyed the warp core would probably breach and that explosion would tear through the shuttle's shields. If the attacker's intentions are just to board the Enterprise then I guess you might be safe from that.