Adding fat to grind for binding purposes is a well established practice, and not only works for elk.
I believe that beef fat will change the flavor less than pork but many people feel pork fat improves the flavor.
I have inquired about grinding the elks own fat back into it and was advised against it. I was not really given a clear reason why not.
Personally I've eaten so much elk for so long that it has begun to taste ordinary. Beef or other game species taste exotic to me now and I've become more interested in various grind changes.