Most likely, Charm Person would not work because it could be classified as a harmful effect, but in all honestly, the magic item is pretty poorly written out, because the creatures created are an illusion, but it "appears real, of the appropriate size, and behaves as if it were a real creature except that it can do no harm.".
This sort of implies that it could do beneficial things, like shoving you out of the way of a charging train, or healing you if the illusion is that of a priest, but those are effects only real creatures can do, and any physical interaction with the illusion reveals them as one. I personally believe that the words "appears real" and "as if it were" strongly imply that these are illusions that act like they're real, but do not have any "real" effects.
It's up to your DM to make clear what they can and can not do, because the item's description did a pretty poor job on defining if it is an illusion, or an illusion made manifest that can actually do things like cast helpful spells.
My personal interpretation as DM would be that the "creatures" summoned by the cards are entirely illusions, they are unable to affect the world in any meaningful way, and while they can certainly look like they cast Charm Person on you, nothing would happen. That doesn't mean you will automatically know that the creature is an illusion however, it might simply mean that you come to the conclusion that it cast something on you and it did not work.