It wasn't at a Hyatt, but I've seen someone walk into a Hilton executive lounge, give their room number, and head over to the buffet. Half way through loading their plate the lounge staff have come over, and apologised, and asked about the guest's Diamond status. When the guest admitted to not having any, the staff explained about the rules, offered to upgrade the guest (for a fee) to a club-inclusive room, then gently guided them out when the guest declined

If you gave the number of an always-club room, you might get away with it. When giving any other one (eg your own number when status gets you club lounge), they almost always will check, even if not immediately.