My suggestion is to speak with the front desk (at least that worked at the Polynesian last month).
When we checked in, my daughter asked whether the tooth fairy came to WDW or whether it was Tinkerbell territory. They told her that Tink would come if she lost her tooth.
Long story short, she lost her tooth, but we were unable to secretly purchase a Tinkerbell souvenir for her, as we were packing to leave a day early (to avoid SNOWMAGEDDON on the east coast).
I went down to the front desk and told them what had happened and to see if they had any Tink pictures. They said that they didn't, but were nice enough to go into the back and tracked down a Tinkerbell - Year of a Million Dreams pin from a few years ago.
We told our daughter that because we were checking out that day, that the hotel would send an email to Tink letting her know that she should come to our house, rather than the hotel room.
Anyway, all's well that ends well.
So... my long winded answer to your short question, is that it never hurts to ask.
P.S. (for jakeandsamsmom) - $20???? We thought that we were being overly generous with $5. Can my kid come live with you until she loses the rest of her teeth?