My son''s band has been invited to do some recording in a music studio in NYC for free on off hours (Sunday Night), should we be concerned at all?

So long as the band or the individual members do not sign anything that agrees that the music studio will own any copyrights in the recording, then the band or the individual members will keep their ownership. However, the studio may claim some rights in any sound recordings due to engineering or input such as beats. If the studio is providing anything to the recorded performances, then the band would want to get a written agreement from anyone who adds to the recording that all rights in the sound recording belong to the band.