I doubt UA would exchange a VDB for a dollar off coupon. But with that said, it doesn't hurt to try.

I know a lot of them don't get used, as people put them in a drawer and forget about it, or only have one and then don't want to go alone or spend the extra money. I heard one time (from a UA employee) only 10% get used, but I find a little hard to believe it could be that low. So whatever the usage rate I doubt they would rather give you the $$ especially since they are so stingy doing it at the gate. If they really wanted to give those instead, they would make it a policy to do it at the gate I would think.

As others said I have never had any difficulty using them when flexible except I can tell you over spring break it is tough (and other holiday weekends etc.). My son has to come home on the Monday instead of Sunday, but with some flexibility finding a Q is fairly easy (generally).

PS: As suggested, look before calling on Seatcounter and you will see the days flights that have the inventory. Might make it easier on you.