I used to play for a dance team. For one number, I'd play the tune once for them to come on, then they would sing three verses a capella, followed by me coming back in as they started dancing. The team were spot-on, every time. Play the intro in C, they start singing in C, by the end of the three verses they were solidly in D and it sounded great if I came back in in D. Interestingly, if I started the whole melee in D, they would claim it was too high, but still finish somewhere around Eb!

Most people who sing a capella drift upwards, it has been commented upon in the past about folk harmony groups and even choirs. It's only a problem if it's noticeable.