For almost every block, it would matter. For log cabins that are strip-pieced, nine-patches, four-patches, or other blocks where every single piece is the same, it wouldn't matter, but as soon as you start making blocks with different pieces in them, like an Ohio Star or a Goose in the Pond, or if you have triangles, you will run into trouble pretty fast.
I don't measure from the cut edge of my fabric. I measure by positioning the fabric straight on the cutting mat and then aligning the markings on my ruler with the lines on my cutting mat. This also keeps my fabric "square", self-correcting each time I make a new cut.