TDD is not really about testing, it's about designing. Doing TDD for your application will make it have a better design (probably) than just doing it on your feeling.
Your problem is : Do you need a good design ? Design is helpful for maintainance and most devs doing TDD consider themselves in maintainance mode just after having added their 1st feature.
On a more pragmatic perspective : if you're the only dev, have very accurate specs and work on this code to do it and never return to it (nor send someone else return to it), I would say that making it work is enough.
But then don't try to get anything back from it if your POC works, and just redo it.
- You can save time by doing an ugly POC and come to the conclusion that your idea is not doable.
- You can save time by doing an ugly POC and understanding much better the domain you're trying to model
- You cannot save time by trying to get some lines of code out of an horrible codebase.
My best advice for estimating how much effort you should put in design (because overdesigning can be a big problem, too) is : try to estimate how long will that code live
Reference : I would suggest you to make some research on the motto "Make it work, make it right, make it fast" . The question you ask is about the 2 first points but you will sooner or later ask yourself the same question about optimization (the third point)