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.
As stated above, it isn't possible because Dogecoin uses Scrypt. However, you could try GPU mining. Their are FPGA implementations and "rumors" of a company attempting to create a Scrypt ASIC ( although due to its memory usage it would prove somewhat difficult ).