Assuming it can run without the battery (which most can but it's considered a bonus feature and a few can't) it will restart, the battery control chip can't switch from battery to constant current mode instantly so it will lose power and then start back up again.
Do not put the battery back while it is plugged in! For a brief moment it will be powered by both the AC directly and the battery leading to a massive power spike in the system. People have done this accidentally and other than the LCD glowing really brightly for half a second no one has had anything bad happen YET but it'd only be a matter of time. Don't do it.