Yes. You can check in at the transfer desk for your UA flight. I have noticed walking by there at that time recently people waiting in line about 90 minutes prior to the 6am flight. Lines can be long (especially for economy). Not sure exactly when UA staffs the transit desk these days, but I would get there no later than 75 minutes prior to departure.

Another option if you don't want to play the transit desk waiting game is go through immigration and check-in at the UA counters. Since you are traveling with only carry-ons, this option would be very quick and painless and could be better (faster, less stressful) than waiting for the transit desk to open and deal with that. It depends on class of service, etc. for the time it would take.