I did this helping a friend move to California. I checked 4 boxes of similar size and took them MDW-SFO. Southwest employees didn't even act surprised. They were happy to check the boxes, but made me sign for damage so they wouldn't be held responsible. I don't think we are the only two people to have done this.

I would recommend packing well, and slightly under-packing. They already know the checked bag/box policy, but it never hurts to bring a printout just in case.

Good luck and report back how it went!