A clay bar removes surface contaminants and will remove the wax, so clay bar first then wax. It won't harm the paint, as long as you use the supplied lubricant and don't get any dirt in the clay to scratch the pain, like if you dropped it on the ground or something.
I had a 95 Taurus SHO and the clay bar did wonders for that. Now I have an '03 GT and I didn't notice that much of a difference, obviously because the paint was still in good shape. It takes a long time to do, the worse the paint the longer it takes, and you have to work in small sections, continually lubricating it with the supplied spray stuff.
I say give it a shot. The worst thing that will happen is you will have a clean car.