Sure it does. Spring rate is the amount of weight needed to compress a spring a certain amount (lbs/inch). If you want a spring to require more lbs to compress, you use fewer coils.
If you take a 10 (active) coil spring and put a 1 lb weight on it, and it deflects 1/2 of an inch, and then modify it to a 5 (active) coil spring, it will now only deflect 1/4 of an inch with the same weight on it.
So yes, wire diameter and outer-diameter are a factor, but if they stay the same and you only change the number of coils, a 5 coil spring will compress more easily than a 4 coil spring.
Todd.K is correct. There is too much in a spring to just specify it by the number of coils. I am going to try out those new Colt springs as I suspect they have the most actual testing.

