No, it shouldn't, but it can determine what happens to the RAW file when it's being opened and converted into something you can work with. Depending on what RAW converter you use, you might have to turn off, 'zero', or disable some of the automatic functions that might be activated by the Picture Style, which is embedded in the RAW file metadata.
Art Knight wrote:
When shooting in Raw File mode does changing the Picture Styles or changing the Sharpness, Contrast, etc. have any effect on the Raw File? Thank you
To add a bit to the correct "no" response above, in Canon's DPP the software will use the camera styles settings as a default starting point for raw conversion, though you can still override that since the raw file itself contains the original picture data and the changes are merely applied to it in post.
Jim and Dan have it right. There is another subtle point, though.
The styles affect the HistoBlinkyMeter: the histograms and the overexposure blinkies will change depending on the JPEG settings which include picture styles. The Raw file will not be affected (as stated above), but ...
... they may cause you to change your exposure.
So, pick one Picture Style and/or other settings (contrast, saturation, etc.) and stick with it. That way you will get to know how your camera responds in a consistent way, particularly how much headroom it has when Exposing To The Right.