If I could legally buy the Mona Lisa, could someone stop me from eating it?

In the United States yes. Only works made after 1990 are protected by the VARA status. Since the Mona Lisa is public domain, there is no protection as a work of art.

Outside the US, however, many nations offer historical relics the same protection we would possibly offer for an old structure in the US. aka. Regardless of the owner, you may be forced to keep the item in its original condition and commit a crime to somehow disfigure it.