Not in my experience. I have both a CVS and a normal grocery store (a Morton Williams) across the street. CVS beats the grocery store on milk price (e.g. Horizon) by ~$0.50/gal and on breakfast cereal (e.g. Cheerios) by ~$1.

Whole Foods 365 brand organic milk is slightly cheaper than CVS, but it's a slightly longer walk and has longer lines and is in a basement, so I tend not to bother. (I probably should go there more often.)