Unfortunately, no....you can't use travel fund credit to purchase the EarlyBird Check-in. It's a completely new stream of income for SWA.
Plus, you lose the money if you cancel that flight or change to another flight with a new confirmation number. Here's a couple of items off the FAQ page for EarlyBird check-in:
"Since EarlyBird Check-in is associated with a reservation, any changes must be made within the same reservation record (same confirmation number) in which the Customer purchased EarlyBird Check-in."
"All EarlyBird Check-in purchases are nonrefundable. Customers who cancel their flight will forfeit the previously purchased Early Bird Check-in option for that particular flight."