They require training for non licensed works as outlined in the approved code of practice. As far as I am aware there is no definitive requirements for how this training is delivered providing the correct content is covered at least in a proportionate way by a competent person. It is probably good practice to record and document any training that is given, but certainly I would say the expectation of training would be beyond asbestos awareness even for minor works.

Asbestos Awareness Training is designed for those who MAY come into contact with ACMs, not for those who WILL, where a higher level of training is required than basic AAT.

If you followed the process identified in a27 Asbestos Essentials for non-licensed tasks, it would not matter if the artex ceiling contained ACMs or not. Of course, if you took samples prior to the work being carried out and the artex ceiling showed NAD, then there is unlikely any need to follow a27.

If it contains Asbestos, yes they would require Non Licensed Training. That would also include the required PPE and the safe disposal of the ACM.
If it doesn't contain Asbestos, no.
With you stating it 'May contain Asbestos', would i be correct if i assume you have had a management survey done rather than a refurb/demo survey?