Corned beef can any cut of beef that's cured and spiced, usually made out of the cheaper fatter cuts like brisket or navel but lean rounds are used too.
I never tried to make a burger out of one but it sounds good to me. Like BIG TWIG mentioned you won't get the meat to bind. I don't think its the fat content but the fact that it's cured and the soluable proteins in the meat that cause the meat to bind together are locked up from the cure. (not sure of the exact reason but I know it won't bind like fresh beef and a little salt.)
If I was to try it (and I probably will now) here's how I'd do it.
Mix some ground beef with cure #1, spices and salt then mix it like you were going to make sausage. Mix untill it the meat starts sticking to your fingers, then let it rest for 12-24 hours to let the flavors balance out and give the cure a chance to do it's thing. Form it into patties and fry them up.
The typical spices for corn beef are allspice, bayleaf, black pepper, garlic and brown sugar. I'm not sure on how much total spice I would use, normally for sausage it would be 1%-2% of the total weight of the batch. I think I'd go 2% and adjust on the following batches.
Sound like an interesting experiment, let us know what ya think of it if ya try it