Congrats on the new job!
I think this is just a developer to management communication “API” issue. 
What you think your are saying gets translated in the manager mindset as being an “additional amount of work” in the project. The reality is that everyone tests their code in their own way; TDD just happens to be a better way. What we are talking about with TDD is automated testing rather than poking around in a debugger, echoing text between lines of code, and hard coding magic values to see how things work.
I really don’t think its necessary to bring up the issue because management cares about shipping a product that makes customers happy, on-time, and in budget. They do not care about how you go about making this happen. Unless you are one of the few unfortunates who has a technical manager who will actually check and see if you wrote tests, just get the product developed in that way that works best for you. Likely, it will involve using TDD methodology and as long as your on-time/in-budget no one will care.
Culture change happens by example, not by debate. Its always easier to ask for forgiveness, after a successful project, than to ask for permission to begin with.
tl;dr: Do it anyway, tell them after its successful, or don’t.