This is such a good approach. A former colleague of mine built an entire scaffolding of integration tests surrounding a test-free system that needed to have a large fraction rewritten. Mocking clients, collaborators and everything.

The tests were only ever used once for that rewrite (the customer terminated the contract shortly after the rewrite was complete, and the entire codebase was thrown into the rubbish bin) but I still think it was worth it. The tests didn't even run that many times because most of them passed at the first attempt but I suspect the effort of enumerating cases had a strong impact on the successful design of the rewrite.

Spend the first four hours sharpening the axe, and so on.