How long does it take to lock in a vote?
The grace period is 5 minutes, which is the same time as the poster is allowed to edit its post without generating a new history.
It may take 5 minutes before the vote lock-in process starts...
But, to answer your question, it takes approximately .000001s for the vote to be locked in. And, up to 100ms for your browser to communicate to the server and get a response of "sorry". Haha.