I did a mental health first aid course through St John Ambulance and the School Board, and the instructor said in absolute terms that this is a bad idea. When someone is hyperventilating, the last thing you want to do is make it harder for them to breathe.

His recommendation is that you give them a paper bag, but put a hole in it. The bag becomes a placebo for them because they see it as something they know is supposed to help them. That stops the hyperventilating because they're panicking and now feel comfortable. The hole is to help them keep breathing.