Often yes, although obviously your mileage may always vary, particularly by the importance of the project (Your old blog? No. A busy e-commerce site? Yes!)

I had an e-commerce system from a long time ago that was developed pre-TDD mania. My post-TDD approach was to develop a suite of acceptance tests for it testing a wide variety of typical use cases (add to cart, use discount codes, check out, tax treatments for various countries, etc.) and this has since saved my ass in a variety of ways without needing to go right down to the unit testing level.

(As an aside, if you're working on a project, need to move super fast and simply feel you haven't the time to do "proper" testing, be sure to do some high level acceptance tests at the least. They will save you time because when the inevitable problems occur, you can just code the process to run automatically rather than be clicking 101 times in the 23rd hour of that 24 hour hackathon ;-))