You can check in from any internet connection. If you need to check luggage anyway, then don't worry if you can't print the boarding pass as you'll be able to print it at the kiosk at the Southwest check-in area or they will print it for you. The main thing is to check in at the 24 hour mark.
I ran into a snafu on our recent trip and was all the way at the back of Epcot (GS is in the front of the park) at our 24 hour mark. My internet enabled phone had a battery problem so I was stuck. I went into the American pavilion and ask the CM at the gift counter if she could give me the number of the WL (we were staying at VWL) and I could then use my husband's (non internet enabled phone) to call them to see if they would do it.
She not only got the number, but called the lodge, let me use the phone right there and the CM at the WL was so wonderful. She took the confirmation number and checked all 9 of us in, printed the boarding passes and then asked if I'd like them left at the desk for pick up or delivered to our room!!!
Wonderful service from both CMs, totally saved us from having to run all the way to GS at the front of the park or having to split up too much on the plane. And bonus... no one had to sit in the last row, where we tall people have knee issues!
I dare say from this experience (and others at various Disney resorts where the front desk has been happy to do this for us) you should have no trouble. Just know your Flight Reservation Confirmation number, and if you won't be near a GS, know the telephone number of your resort!
Have a great trip.