A week would be ok, until the end of the month, not legal, but documents take 3-4 days post at these times so cant always be done instantly.
However, what are you going to do at the end of the month, decalre it sorn anyhow or hope it sells?
Not many people will buy a car with no tax, tax and test adds hundreds onto a cars value...how are they going to test drive with no tax or insurance? Remmeber, YOU need insurance on the car for them to drive it 3rd party.