Well due to these RTW tickets I've got a few experiences of impressive checkins, aka a lot of boarding passes being printed: In this specific instance my LHR-DFW-LAX-JFK was considered one trip by AA (14 hours in LAX isn't a stopover) so in LHR I was checked-in all the way thru. After the change from LAX I was given boarding passes for LAX-JFK-YYZ-HKG. Ultimately in 58 hours I did all those segments and ~14k nmiles. So whether online check-in, or at a desk, you will still be considered checked in.

A similar one I was very "proud" of after the great LHR fire IRROPS I printed out SEA-LHR-MAN-LHR-DOH-HKG on an AONE at a desk, again, no stopovers just "transfers", we were all impressed (I lost a stopover in the UK, and a nested LHR-BAH-LHR , but kept my QR F segments).

Personally on RTW tickets I often try to do an check-in as a backup and to see if there are problems... I've had the AA desk forget to properly re-ticket with changes a few too many times to want to do that when there is a risk the AA desk is closed, since I live in Asia. 99% of the time go to the airport check-in desk anyway to get my paper boarding pass after too many issues with digital passes or phones in less popularly visited airports. CX, my home carrier, trains me well on this point anyway - if I do pure OLCI I can't board the plane without them doing a physical check anyway, so I may as well do that earlier on.