We seem to be confusing two very separate services here.
The OP is flying Southwest and was merely asking if there was any way to check-in online 24 hours in advance. This can be done by Lobby Concierge (formerly Guest Services) at any resort or at Guest Services at a park or DTD.
There is also a Disney service called Resort Airline Check-in (RAC), in which people flying on one of a select group of "participating" airlines can check-in for their flight AND check through their luggage to their final destination. RAC is exactly like curbside check-in, only it's in your WDW resort lobby and not at the curbside at the airport.
RAC is very different from checking in 24 hours in advance with your airline in order to get a favorable seat assignment. RAC can only be done same day, and the transaction must be completed no later than 4 hours prior to flight time. The RAC desk at each resort is open from 5:00 a.m. to 1:00 p.m. This means that anyone on a departing flight before 9:00 a.m. is inelegible to use RAC even if they are flying on a "participating airline" (and since the transaction takes several minutes and must be completed by no later than 4 hours prior to flight time, for al practical purposes you really can't use it for flights that leave before about 9:15 a.m.).
Southwest is not one of the "participating airlines" and thus the OP is not eligible to use RAC.