As someone who has done exactly that...well, honestly, as long as there weren't many stairs it wasn't too much of a problem. Before I had my office in the lab, I did bring the Brommie everywhere. Yes, even into the restrooms. In between buildings, I just unfold and ride (it saved me a few minutes, especially if my next class was way across campus), unless the building is right next door, in which case rolling works just fine. I have the M6L (no rear rack) and it rolls perfectly well if I leave the handlebars up and use it like a pushcart. I did change the built-in caster wheels to scooter wheels though, which made the rolling so much easier.

If you're worried about wrangling your bike and a backpack or other luggage at the same time, I strongly suggest getting the integrated front luggage system. That is the best thing ever, I swear. I have the Brompton S-bag for everyday use and a bigger Carradice bag. I also added a Klickfix seatpost mount and a Klickfix basket for the times when I really need to haul stuff. If you're concerned about the price, ask Folderfanatic about making your own luggage that will work with the front luggage system. She also makes a nifty bike cover (which she very kindly gave me one of!), and I'm pretty sure that with a little cutting and sewing, you can modify it to have a hole on top that you can poke the saddle out of. The official Brompton cover does have a hole that you can use for that purpose, as shown in this video: