I stopped using gauze only ten minutes after a wisdoms tooth extraction. Will a blood clot still form? Or will I get dry socket?

Dry Socket. Blood clot will most likely form. The gauze does not prevent the clot from falling out. Avoid gargling and rinsing aggressively for a few days and you will probably be fine. Any problems please call your surgeon.
No relation. Normal bleeding time is 6 minutes, after which the clot should be formed, follow by ingrowth of granuloma tissue . Dry socket is caused by infection occurs which lead to losing a clot. Dry socket if occurred, starts in day 3.