Not by definition. Of course spring rate is not linear anyway so as the spring compresses it takes increasingly more force to continue the compression.
You are correct on the constant22RToy said:As long as the additional force required is directly proportional to the deflection, that is linear. F=kx. Spring rate k is constant.
In a progressive spring, the rate is a function of the deflection, say F=(k+.1x)x. As the deflection increases, the spring rate increases.
Of course, this is all in theory.