I've taken framed oil paintings through, but I can't remember taking anything covered with glass. I would assume it would be fine.

I wrapped the art in bubble wrap, sent it through the X-ray machine, and no one asked any questions. I did secure the bubble wrap with a minimum amount of tape in case they asked me to remove it. <shrug>

On the plane, the FA helped me store the picture behind the last row of seats (once at the back of coach on a regional jet, and once at the back of the first cabin on an MD-80). Occasionally there is closet space available, but I actually feel it's more secure behind a seat, where no heavy suitcase can bang into it.