I do, but I only use enough mayo to bind. I also add sweet relish, generally.
I add enough mayo to bind it, sweet relish to taste, (and onion and celery) then thin it out with a little Miracle Whip. That works better than using all mayonnaise or all MW. I do the same mayo+MW thing with devilled eggs, but those get some yellow mustard too.
The cold cut combo sandwich is made with turkey cold cuts. If you want real cold cuts, you pay extra for that; i don't remember what they call that one.