are your struts the OE ones that came with the car? if so there is a lot of miles on them and you should replace them before getting those springs.
if the spring rate is about the same, then you should be OK . the stock dampeners are designed for the stock spring rate. the spring rates for your car (assuming it is a manual) 163 front and 119 rear. the springs you want are 196 front and 186 rear. your rear struts will go first because the spring rate is increased significantly higher. in a nutshell i would get new struts as well.
Dom Tuned 2003 WRX Wagon
If it's worth doing, it's worth overdoing