I wouldn't count on it working. The staff at the location do not have any access to member credits, and thus, free days. If you were to get it attached, you'd probably have to go through customer service, and even there it's doubtful.

I have, however, done the reverse. I had a car booked on a free day, then learned after picking it up that the dealership I'd taken my own car to would pay for the rental, billing to them directly. Naturally I didn't want to give them the benefit of my reward day, so I asked the location if they could just remove it. The counter agent took the "coupon" off my rental, but of course the free day had now vanished. A quick e-mail to customer service with both my original reservation number and RA number got it re-instated though.