Right, if you do OLCI and it works (big IF, as it works about 50% of the time for us), you can go straight to the room. We took the ME to BLT and dropped our bags there, and checked in at the desk there, because MIL was with us and wanted to link a separate credit card to her MB (mine and DHs were already linked). Then we took our "park bag" and walked over to the Contemporary to get the stroller and scooter and head out onto the monorail for lunch. On departure, we scheduled breakfast at The Wave, dropped our checked bags off, ate breakfast, and went back to the room to use the bathrooms, take our carry ons, and get a final printout of our room charges from the desk at BLT.
ETA: DH dropped off the scooter for his mom the night before; she can walk pretty well for her age.
I have checked in for BLT at both the Contemporary and at BLT. If I don't have business at the Contemporary, I have found it easier and nicer to check in at BLT - there is almost never a line and it's quieter and more peaceful. I think the one time I checked in at the Contemporary was because we had a known issue - maybe MB wasn't working or we needed to do something with our tickets, I can't remember - and we were already at the Contemporary so I decided to deal with it there.