Absolutely, if you don't need funding for first year but the adcom thinks you could handle the coursework, they are much much more likely to give you an offer of admission. That's your chance to show you can handle it.
However, you'll need to be one of the best students in the program to then receive funding down the line. Funding is a commitment for many years to students who come into a program. It's a risk departments take to get people in the door. The idea is that a handful will turn out to be great. They probably wish they could just get rid of the weaker students after two or three years. However, they have to have more than just the very best students complete the program for a variety of reasons... would you attend if only 3 or 4 out of 20 made it through?
Essentially, the problem is they don't know in advance who they should fund so they fund "too many" students. If you aren't one of the top people in you cohort after a year or two, you might find it quite difficult to secure funding.