It is quite possible. The whole point of carbon dosing is to encouage bacterial growth that will take up nitrate and phosphate. UV will potentially kill bacteria passing through it so in that respect it would be counterproductive. Basically you would be growing bacteria to take up nutrients, then at the same time killing bacteria releasing those same nutrients back into the water colum. As far as how long to wait, I don't think that would matter much, it'll be just as counter productive in 6 weeks.