What a thoughtful question! No. They can get them funded but expect hiccups. The problem here is that hiccups can cost a boat load of money over the next 87 days. As a lender, my recommendation would be to put tight financing contingencies on every contract (even if you like the loan officer) and press the loan officers to send the closing packages out early (if they say they can't do this, they're lying). Tell the loan officers to use you as the contact for entry on all appraisals so you can know when that is getting done.
Good luck Michael. It's going to be a fun 2 minute drill!