Is there a workable approach to use test-driven development (TDD) in a COBOL application?

Maybe check out QA Hiperstation. It could cost a lot though (just like every other mainframe product).

It only used it briefly a long time ago, so I cannot claim to be an expert. I used it to run and verify a battery of regression tests in a COBOL/CICS/DB2/MQ-SERIES type environment and found it to be quite effective and flexible.

I would say this could be one of the pieces of your puzzle, but certainly not the whole thing.