Well, I went to the source, and yes I can pre-board. You get A B or C based on when you did your checkin. From southwest.com:
Checkin Procedure
Customers may check in for their flight and receive their boarding pass and Rapid Rewards credit online at southwest.com (for eligible reservations only), at the Skycap Podium (in select locations), Ticket Counter, Departure Gate, or RAPID CHECK-IN Kiosk (where available).
Customers who are age 65 and older and traveling on a Senior fare must be age verified in order to request their boarding pass online. Visit our Travel Tips for Seniors for more details on how to become age verified.
Customers may check luggage and receive boarding passes at the Skycap Counter (in select locations) or Ticket Counter up to four hours prior to scheduled departure.
To determine the best time to check in for your flight, please refer to the Airport Arrival chart. The Departure Gate opens for checkin and boarding pass distribution one hour prior to departure.
At 20 minutes prior to scheduled departure you can get a boarding pass only at the Departure Gate.
Passengers who do not obtain a boarding pass and are not present and available for boarding in the departure gate area at least ten minutes prior to scheduled departure time may have their reserved space cancelled and will not be eligible for denied boarding compensation.
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Boarding Procedure
Each Customer will be issued a boarding pass grouped by A, B, or C (in that order) based on when the Customer checked in online at southwest.com, at the Skycap Podium, Ticket Counter, Departure Gate, or RAPID CHECK-IN Kiosk (where available).
Prior to general boarding, Customers with disabilities, unaccompanied children between the ages of five and 11, and adults traveling with a child under five years of age will preboard. Customers who choose to preboard cannot sit in an emergency exit seat.
Because Southwest Airlines maintains an open-seating policy, general-boarding Customers may sit in any open or unclaimed seat. Customers holding boarding pass "A" will begin general boarding, followed by Customers with boarding pass "B," and then "C." General-boarding Customers who choose an emergency exit seat must meet all requirements set forth by the Federal Aviation Administration and Southwest Airlines.