are rec letters important for recruitment?

Only initiated members may write a recommendation for a pnm to join their sorority. They almost always come from alums, although some sororities also accept recs from current actives at different chapters from where you are rushing. Each sorority has their own rules about this and their own form online for the rec writer to use. So unless your coaches are alums, they can't help you. Yes, they are important to keep you from slipping through the cracks. You need one for each house. Get recs for as many houses as you can.

Unless it’s from a current member of that chapter, don’t waste your time. Letters of rec really won’t make a difference it doesn’t matter if your coach/aunt/second cousin was in the sorority everyone can find a link to a sorority if they want

Rec letters will only really help you get through the first round! They aren't super important. I didn't get any but still got one of my top houses