Yes and no. Info about the picture style is saved in the CR2 file and DPP can read that info to give you a default RAW conversion setting similar/equal to the one used in-camera (for the JPEG-preview). But it doesn't affect the binary image information captured by the sensor - you can easily switch between picture styles in DPP and get the exact same results as if another picture style was chosen in-camera.
One important thing about a possible effect on your RAW files has already been mentioned by Neuro: If you want some histogram assistance for exposing as bright as possible without blowing highlights ("exposure to the right") you should avoid some things. I've found that if I choose picture style faithful and turn off both ALO anf lens correction, I get a better indication in the histogram for when I'm really approaching the right side. More contrasty picture styles, ALO and lens correction all tend to brighten the JPEG-previews. And for some scenes this can make a real difference for the final result. (Of course, another way of achieving basically the same could be to accept a fair amount of highlight blinking in the JPEG-preview. When those files are "blanked" in DPP, Lightroom etc they will be noticeably darker and with less/no blown highlights.)