It's a good question.
Basically I would say yes it's possible to CE mark under medical device directive, and without involvement of a notified body (i.e. a Class I medical device).
Although it's intended purpose is not fully specified, it would be in the same category as other broadly applicable devices, like a general purpose syringe.
The problem is, though, that the CE marker probably would not have really checked all requirements in the regulation. They most likely just did a 601-1 electrical safety and possibly the 601-1-2 EMC test, extracting the relevant clauses to a power supply, and that's it.
Those familiar with the directive would know there are a bunch of other things like marking and registering EU reps, marking date of manufacturer etc. So the absence of such marking might give a hint that it's a bit of a fudge CE mark.