This could potentially work. You could run the sales as daily flash sales, letting buyers know about the purchase thresholds that have to be met before a sale becomes final. I think if you didn't run these as flash sales with time limits, it could take too long for a given product to reach it's threshold. People want their stuff fast. The flash sale concept would both encourage purchase via natural urgency, and enable the sales to be finalized and processed quickly.

If you can guarantee manufacturers that you'll hit their minimums, they will be likely agree to this as long as they are okay with drop shipping the sold goods.