It could, but as someone who has spoofed user-agents in the past (primarily to get Chrome-only websites to cooperate) I would prefer if it wouldn't. If the baddies can snoop my https traffic or directly copy the auth cookies from my machine then also copying my user-agent isn't that big of a step for them. One might argue that detecting changes in user agents could be part of some kind of defense in depth strategy, but as a user I imagine I'm already so boned in that scenario that I doubt it would save me. So overall such a mechanism would bring me more inconvenience than security.