Before COVID-19, with no luggage to check, I was able to check in and get the DOCS OK boarding pass in hub lounges (like MSP) most of the time, but if the situation of admissibility was complex, they would send me to the gate to do this. Lounge agents didn't feed confident about reading and interpreting complicated rules on TIMATIC, although often a GA does a final check anyway at boarding time.

ADDED: Obviously I had already done OLCI and printed my boarding pass (without DOCS OK) to get through TSA airport security, but part of doing that is that you get a message that you must show passport etc. to a DL airport agent no later than one hour before scheduled departure time (presumably of the international segment, as I've checked bags at MSP for domestic connections to international flights at T-30 rather than the T-60 required for international). I'm not aware of passengers being offloaded for failure to do the document check by T-60, but it would be a nice excuse if a flight is overbooked.