The windshield will be a weak point, but I don't think it will "fold like cardboard". The Mustang convertible has a very high rating for crash and roll over.
But you will lose pretty much any back seat usefulness - the back bars will be very close to the head of any back seat passenger. While you can pad the bars, it will be a hard surface still.
This is my roll bar (well it was in my 2006, and will be modified for the 2013 to fit with the CDC light bar now). For drag racing I had to use a 6 point cage, with harness bar. So there are two swing out door bars. If you aren't tracking the car then you can get by with the 4 point.
You can get a sense of how close the back bars are to the heads of any passenger back there
The fabricator did a different set up for a friend, and his back bars are a little further out. It required cutting up the top of the "sill" on each side so that the main hoop bars could go inside that area, but allowed him to move the back bars out some: