As far as i was aware, if the car has been taxed (i.e ran out the month just past) and you have applied for a new disc online, you have 5 days grace period into the new month for delivery of the tax disc. In which you can drive on the road. I think the police can report you to the DVLA, but if the DVLA see you have purchased tax and it's on the way they won't have any problems with it. I have driven like this several times and had no problems what so ever.

Edit: to say in your case you won't be able to drive i don't think.