15th club in bag ruling

No, they couldn't, as Spuddy has said, but if a player deliberately tried that on, thinking you could be disqualified, he should be disqualified under R33-7 and, I'd argue, be subjected to club discipline as well.

By the way, the penalty for having more than 14 clubs is not disqualification. In stroke play, it is 2 strokes for each hole before the breach was discovered with a maximum of 4 strokes; in match play it is loss of each hole before the breach was discovered with a maximum of 2 holes. Once you discover you have more than 14, you have to declare a club or clubs out of play. If you then used the club, the penalty is disqualification (R4-4c).