What benefits does studying jokes in your L2 provide? I'd think that it would only provide you with a better understanding of culture, puns, or wordplay, but is there something beyond that?
One popular view of verbal humor is that it comprises utterances that violate (deliberately but benignly) one or more of the principles of communication, and that a good way to characterize those principles is by the 4 Gricean Maxims (e.g. PDF). Each maxim is a statement of some aspect of communication that should hold in order for the communication to be successful. They are
- Quantity: The amount of information is neither too much nor too little.
- Quality: The information is true.
- Relation: The information is relevant.
- Manner: The information is expressed efficiently.
The first three relate to the information being conveyed, and therefore should be language indifferent. The maxim of manner, however, relates specifically to, well, the manner of expression, and therefore will very often be maintained or violated on the basis of a feature specific to the language of discourse.
I would expect that humor owing to manner maxim violations only could be productive to study in a second language as a distinct avenue to comprehension. This could help to distinguish subtleties of what - otherwise well-formed - phrases are considered inefficient at expressing a given idea. For example, they could point out lexical ambiguities as in puns, words whose mere appearance is considered too sophisticated or esoteric for casual conversation, or phrasal connotations not readily available in a glossary.
I'm not sure how easy it would be to filter one's humor consumption on the criterion of violating only this principle, as a learning aid. But it could provide some guidance after the fact in deciding which jokes warrant further investigation.