Don't skip class for recruitment!
Talk to your rho chi or the greek life office, and make the situation clear, so that it doesn't look like you dropped out because you didn't turn up one afternoon.
I'm not sure of the specifics of FAU's recruitment, but if you can arrange split parties, that might be a good option. Or if it's a later round of rush and you get only a few invites, maybe you can get your "breaks" scheduled during the time you have to be in class.
You can also talk to your professor or someone else in the department to find out if there's another section of that class that doesn't conflict with rush and that you can attend that week.
Good luck!