Yes, you can. Boxes have the same size and weight limitations as standard suitcases
Here's the policy:
Southwest will accept the first two checked bags for free provided that the bags do not exceed 50 lbs and 62 inches (L+W+H). Overweight items from 50 to 100 pounds and oversized items in excess of 62 inches but not more than 80 inches will be accepted for a charge of $75 per item. Only one $75.00 charge applies if the piece is both oversized and overweight, regardless of the weight as long as it does not exceed 100 lbs. Excess baggage which is also overweight or oversized will be charged excess baggage plus the applicable oversize or overweight charge.
One additional item to note is that some locations may have periodic resitrictions/"baggage embargo", especially during the holidays. One is planned to be in place for Montego Bay from August 16, 2019 through September 16, 2019 (see the link provided by @TheMiddleSeat) -- if that is your destination and timing then boxes are not allowed.
Southwest customer | Home airport DCA | Community Chamption