FWIW, I just checked the cooler with a short piece of frame tubing and if your frame tubes were 47.5'' C-to-C the cooler handles would set on them in such a way that the frame would support it properly. So, I take back the statement that I would not use the handle to support the cooler.
You probably saw on my other post that this is a heavy cooler. With food, frozen in ice for a GC trip, it's a freakin' super heavy cooler. It took 4 people to safely load it onto the cat at Lees Ferry. Depending on your use, you might want to take that into consideration when planning on supporting it by the handles. Just a thought.