They can ring the insurance companies to see who is covered for what, so unless it was 3am, they could have sorted it by the roadside. Basically, if it was covered, regardless of the MID, nothing will happen.
On another cheery note, saw on the tv the other day that they will seize cars now if the tax is 2 months and a day out of date.
We've had a few cars clamped recently parked outside on the road for no tax. We even had one clamped outside the tyre fitters on a private business park.
The DVLA have subbed it out to a private company who are obviously on commission