An interesting idea. You might be able to convince them of a Chroma Skin or something equally as low impact. Perhaps even link it to data they have based on your playstyle?
You played Master Yi the most this year? You get that Chroma skin on your birthday.
The players that try to 'game' the system by either broadening the different potential skins or focusing it down to one champion in particular will be more inclined to obtain specific products with RP (Champions for people going the broad route, skins for this 'main' for those going the focused route).
Obviously if you either already Own the Chroma Skin it goes to the next played champion for their Chroma.
If you own all the Chroma skin, roll back to the most played for the least expensive available skin for that champion. If you own all of those cycle through each champion that fits that bill.
If you somehow own all champion skins available, potentially a skin in the vault that isn't a player reward (Riot's already made it clear the Beta/Pre-Order/Magazine, the Old Pax Skins, and Ranked Rewards skins are super off the table for Essentially Forever).
If you're one of the rare few who has poured that much money into the game to have all the skins available and in the vault (which implies you have some, if not all, of the Rewards skins), well, don't have an idea on how Rito can reward those handful of people.
Edit:
As others are addressing, yes there is huge codework built into it, and my thought is under the supposition that entering in your birthday in this fashion would set it in stone to prevent the 'every day is my birthday' abuse users could do.
