You can indeed use a brown wig with colored sharpies, but you'll probably need to test swatches because the results can be unpredictable. This thing right here
was a light brown (color 8 specifically) wig colored with lime green sharpie in the ancient hand method. An unorthodox combination, but it yielded the dark brown with green highlights color that I was after. Just make sure to rinse; I forgot to rinse that thing and I ended up with my pretty white shirt stained with lime! (Thank god for bleach pens.)
Honestly, for darker colors, starting with white = not a good idea. Get a swatch ring and have fun!