Email for late / not received offiline payment

Could there be a setting to automatically send an email out to registrants that have chosen offline payment, but we have not received it yet? I usually put in my email bodies for offline payment that payment must be received within 10 days or their registration will be cancelled to make room for other registrants. (We usually don't cancel them, we just need a reminder for them to pay.) This could also be integrated with Jamie's request for a "sign up now - pay later" function - if they don't pay within X days, it will send a reminder out. (And that email could BCC to the admin so they know.)

I just suggested something similar in response to Jamie's post Sounds like a good idea.