Yes you can. From your description the project is in a good shape - solid amount of functional tests automation is a way to go! In some aspects its even more useful than unit testing. Remember that TDD != unit testing, it's all about short iterations and solid acceptance criteria.
Please remember that having an existing and accepted project actually makes testing easier - working application is the best requirements specification. So you're in a better position than someone who just have a scrap of paper to work with.
Just start working on your new requirements/bug fixes with an TDD. Remember that there will be an overhead associated with switching the methodology (make sure your clients are aware of this!) and probably expect a good deal of reluctance from the team members who are used to the 'good old ways'.
Don't touch the old things unless you need to. If you will have an enhancement request which will affect existing stuff then factor in extra time for doing the extra set-up things.
Personally I don't see much value in introducing a complex infrastructure for mock-ups - surely there is a way to achieve the same results in a lightweight mode but it obviously depends on your circumstances