A burger made from pastrami
It strikes me that it would be a bit overpowering, and that even with a binder you would have a hard time keeping it together. Cured ground beef just seems like it would be nasty :-)

I've experimented myself with two 'inclusions' in fresh beef patties. One is bacon (cooked), the other is salami. They are both interesting, and if minced finely and added to the grind they do not interfere with texture but add some excellent flavors and saltiness.

I would imagine pastrami would give you a nice result as an inclusion too. I'd chop it up and mix it in with the cubed up beef before you run it through the grinder.

With burgers really the fresher the better. I grind about 2 hours before grill time, and that is only so I can throw the patties into the freezer. I like them thin and cooked through, so I need to freeze them so they hold their shape better during the first side cooking. If you like your burgers to have some pink you'll probably want to skip the freezer.