Well, strictly, detergent won't strip the DWR, but it will negate its effect. But yes, you can add DWR to any fabric that will take the treatment. If it's already been detergent washed, give it a couple of soap washes to remove detergent residue before applying the DWR treatment.
Don't expect waterproof performance, though; it will only be water resistant, and, depending on how open the weave is, raindrops may still force their way into the fabric.