Yes, it will work. As Maryann suggested, use many attachment points -- not only to limit weight on any single attachment, but also to provide good overall support for the rug.
I suggest a line of attachments across the top, about 2" apart. Add another line of attachments about 4" apart, 1/3 down, and again 2/3 down. Also add a few across the botton, to keep it from flapping.
The extra lines of attachment will relieve stress on the upper attachments and keep the rug from sagging. All of them will be loose enough to allow expansion & contraction without wrinkles.
Be sure to use a sturdy mount board. I suggest a 4-ply matboard with 4 mm polyflute reinforcement. Poke the Attach EZ attachments through both layers.