I don't this it's a very good idea. When people use faucets, it's because they want to get some coin which already has some value. Nobody want some intermediary yet-another-random-altcoin between them and the faucet.
IMHO, people just wouldn't use faucets which would be paying in your coins.
Ya that is true. I was thinking, say someone wants litecoin and bitcoin, but they don't want to keep track of and use numerous faucets. They could use the few faucets that pay in my coin, and then the users could trade out my coin for the coin that they choose from the faucet site, or just get a payout and exchange it on trading sites. In my mind it would create more freedom for the user and could possibly bring more attention to the faucet.