Depending on what DWR is chosen, it is certainly possible. Some are mearly hydrophobic coatings, some are heavier, more like a plastic film. I believe RainX (heat activated kind) is heavier than a silicone coating like Camp Dry. I have used a DWR on my shirt, and, it was also dipped in permethrin. It works, sort-of. But mosquitoes bite through the shirt, anyway, more for black-flies, no-see-ums, etc.
My own nylon pants are usually dipped in permethrin, allowed to dry, rinsed and then laundered. Permethrin acts like a DYE. Sort-of like a blue dye on cotton cloths. It sticks to the molecules of nylon with loose hydrogen bonds. It is not really a repellant. Except, any insect that has a survival instinct will tend to avoid it. Kind-of like swatting a fly…they move. Mosquitoes, no-see-umms, etc will do the same. If they are hungry enough, they will bite immediatly, right through a more open weave like my shirt, but they become preocupied with wiping off that "bad" substance right away, the second they start feeling the effects. They need to survive to lay eggs… I think of it as *revenge*, not repellancy, ha, ha.
A DWR is a COATING. It does not bond with the nylon molecules. It simply makes the molecules more hydrophobic. The two can certanly be used together, provided you treat the fabric with Permethrin, first. Dry it, rinse any excess, then launder it. THEN spray DWR and dry it in the dryer. However, heavier coatings will mask much of the permethrin. You need a good heavy dipped coating with .025-.05% saturation throughout the fabric to prevent this masking. Campdry, NikWax TX, or one of the non-heat activated ones are not as durable, nor are they as heavy, and would be a better choice.