If it takes longer then expected you request an extension of the appraisal contingency. if the seller says yes no problem. If not then you get your deposit back and everyone walks away.
As I said above, if you have other contingencies to lean on and the home does not appraise then use one of the other contingencies. You do not have to be specific to the seller, there is no obligation. Just make darn sure you do it in the time frame you are alotted per the rpa.
Since you have removed the appraisal contingency then at day 17 or whenever your other contingencies expire you must fish or cut bait whether you have the appraisal number or not.