No account needed. Just the confirmation number and name. I don't even recall if it's an option to pull up a confirmation number from a Southwest account. All airlines work this way since not every passenger sets up an online account and many purchase through travel agents or other booking services. You could even check in at the airport, although most people don't go to an airport early enough to get a low boarding number.
https://www.southwest.com/flight/retrieveCheckinDoc.html
For the OP, we're just advising that you should try to check in as early as possible. That would get your group a lower boarding number and possibly a better chance of getting seats together. Seating on Southwest is first-come first-served like boarding a bus. They have that Early Bird Check In for a fee, as well as Business Select where they reserve the lower boarding numbers.