I wouldn't count on it working out too good.....to the best of my knowledge the NEH is a "sight hound", that is to say that they run the animal more by sight than scent. Not knocking your dog here, but running after an elk they are looking right at is a different ball game entirely than treeing a raccoon by nothing but scent. The NEH does follow some scent to a degree, but you've got a very large heavy animal that produces a lot more scent than a 15 pound raccoon. Raccoons are chased up a tree by a dog that follows scent, and there is generally not a whole lot of it, so the dog has to have one heck of a nose on him to get the job done.
Try it, you might have a dog that can tree more raccoons than any other dog alive, but I wouldn't bank on it happening......there's a reason we use the breeds of dog that we do for treeing raccoon.
Still, no reason you cant have some fun and try.
Edit: I am leaving out the part about having instinct to "tree"....the coon hound breeds are referred to as being "tree hounds" because they will {not always, but they are supposed to} stay at the tree the animal went up and bark to, A. Keep the animal treed....and B. Call you to the place where they and the game are. While a beagle, for example is a scent hound it has zero instinct to tree. As far as I know the NEH has no real tree instinct and never had any real reason to have it...elk don't climb trees. When you say he "trees squirrels", there is a big difference between seeing a squirrel run up a tree and barking at it for a few minutes {if that long} and running by scent to a tree and then staying there and barking {for as long as it takes to get you there} at an animal that the dog never sees and only smells a very little amount of scent. Good luck.