The main problem is that once someone has made the decision to call, they've made their decision - a 15 minute hold isn't going to bother them much, and they certainly aren't going to do anything but sit there holding the phone.

If, instead, they had said "we'll call you back in about 15 minutes" and at the same time sent an email with chat/self help options it might have worked, because then you DO have 15 minutes to dick around.