The vehicle should be licensed
If the number plate you are selling is on a vehicle, then the vehicle should be taxed. The DVLA will still consider your application if the donor vehicle is not licensed, provided the license expired less than 12 months ago, and was declared as SORN straightaway. If you applied for a tax refund, however, then you cannot sell the number plate.
The vehicle should be MOT’d
If the number plate you are selling is on a vehicle, then the vehicle should have an MOT. The DVLA may decide to inspect your vehicle, so expect to be asked to produce it at the nearest DVLA office.
You will not need an MOT if your vehicle is not old enough to be tested.
So yes, and you won't be able to cash in the tax either.