Of course you can do that but you enter another level of negotiation because you are quitting and it might not even count toward the budget at this point. I would not recommend doing that every year as a negotiation tactic either.
I tend to agree with Redwards, and unless you are working in a small company if you do your job correctly it becomes more a political game than anything else.
I've had success in getting promotions for some people when this sort of thing happens... sometimes it's a wake up call for the execs to light up a back burner conversation with HR.
Other times, I've gotten a shrug.
Pretty sure that in the current era there isn't a "S" at yearS for someone decent (and willingful).
Most companies are perfectly fine to hire/poach from elsewhere whereas most companies are sucking at retention (that is, if not actively pushing people away). The combination is an aggressive environment.
If management truly wanted to "negotiate" then they would begin putting conditions on a raise or something.