Yes, you can tell if they are fake or not in this game.
http://www.thonky.com/animal-crossing-new-leaf/paintings-works-of-art/
Zoom in with camera and look for the details mentioned on that page. I've had Red only have 1 real piece 2 weeks in a row (first week he had 2 real).
That's some really cool detail. I'll be using this for future reference, thanks!