I don't know that there will have been much rigorous study regarding the benefits of multi-programming language exposure on overall programming ability, but I would argue that the studies regarding why learning a foreign human language (which you may never use in practice) is beneficial would in general hold equally well for studying foreign programming languages. The benefits ascribed often include improved cognitive abilities as well as improved understanding of one's native language.
here's some links to studies
anecdotally, I complained a great deal about taking COBOL, and have never really used it but was able to apply things I learned in that class at my first job.
