The easy answer to this is Yes. But you may need to use waste canvas if you want to keep your stitches completely even.
If you have a relatively coarsely woven fabric and can see individual threads well enough to count them, you can work counted techniques directly on the fabric. Keep in mind if you choose to do this, that most fabric (unless it’s manufactured specifically for counted work) is rarely the same count horizontally as it is vertically. It may, for example, be 47 threads per inch on the warp (vertical threads) and 36 for the weft (horizontal threads).
This means that square stitches when counted regularly will stitch as rectangles. Your entire design will look like it has been stretched out in one direction or the other. This effect can be really effective, especially in geometric designs for borders and such. But if you want your design to match your chart, your best shot is to use an evenweave fabric or tack down a piece of waste canvas and use that as a guide to stitch over.