I am sure you could refuel just so as to warm up the fuel,wait an hour or three,and then do the drains.But as spanners says,no point in refuelling prior to a service and then doing the drains.
I regularly pull 3 litres or more from the inboard tanks each day,so it shows how important to do them religously.This also depends on where the aircraft operate and what the ground tanks are like in foreign ports.