Can a Butterfly Jalapeño be used to mine dogecoin? If so, is it cost effective, compared to it's bitcoin mining cost effectiveness?
No, the Jalapeño is a Bitcoin miner, it solves the SHA-256d hash function.
On the other hand, Dogecoin uses the Scrypt hash function. The two are not compatible, and as far as I know there is no Scrypt ASIC being sold, yet.