It depends on how long the checkin counter will stay open before a flight. Once you checked in, I believe the airplane will wait for you for a reasonable period of time if there is delay in immigration and/or safety check. I assume it is 60 minutes for international flight. But on my last standby trip to Singapore on SQ, I did not get my boarding pass until exactly 30 minutes before departure. So SQ checkin counter open until 30 minutes before departue, I am not sure exactly how long for UA.