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Can a Butterfly Jalapeño be used to mine dogecoin? If so, is it cost effective, compared to it's bitcoin mining cost effectiveness?

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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.

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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 ).

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