No, they don't. It is, however, the only scenario that would make sense if someone who had passed the competency test was flying a drone without the registered operator present in order to avoid unnecessary aggravation - not generally a good idea when the police are involved. If that individual is challenged by the police, to ensure full legal compliance a suitably informed member of the police would need to establish:
- Whether the Operator ID is correctly displayed on the drone
- Whether the Operator ID is valid
- Whether the pilot has passed the competency test
- (Potentially) whether the pilot is authorised to fly the drone by the Operator
Buried in the CAA's blurb is the fact that the first two can be achieved by contacting the CAA (no online apps yet) and passing on the Operator ID, and a cross-check could also be made by asking the flyer to confirm the details provided by the CAA. The CAA should also be able to confirm the third on the same call *IF* the pilot can provide their Flyer ID, which in most cases should be sufficient - there's probably either going to be a friendly "fly safe", caution, or an arrest at that point. If one of the latter two, then contacting the Operator can happen whenever.
If the Flyer ID isn't available, then that's going to involve the Police calling the Operator to confirm the pilot is authorised and competent, e.g. additional hassle for the police officer, and less likelihood of getting away with a verbal warning if there was a potential breach of the law.