So I just came back from vacation and yes, you immediately get the free bag for you and your travel companions booked on the same flight. You also immediately get zone 1 boarding for you and your group.
I applied and was approved about one week before I flew out and did not receive the physical card until sometime while I was on vacation.
Dumb OT Moment: This was my first time traveling with NEXUS that automatically confers TSA Precheck. I did not have TSA Precheck before. It wasn't explained to me that to use the TSA Precheck with NEXUS, I have to add the TT number to the actual booking/boarding pass. I did not get my NEXUS card until several months after I booked and when I checked in there was no option to add the TT numbers to my husband and daughter when I checked in together, so I didn't think anything of it because it is automatic right? LOL, NO. Well, got that sorted out for the return flight anyway. Lesson learned. Call the airline if they give you no option to add a TT number at check in.