"I've heard rumors out there that a split finger fastball is very hard on the elbow, since it strains the tendon that run from your hand, through your elbow, and into your shoulder. By splitting your index and forefingers, you put a strain on that tendon. Is this true, is there a good possibility of elbow injury in throwing a "splitter"?"
While you can hurt yourself throwing any pitch, whether you hurt yourself or not doesn't depend on whether your fingers are split or not. What matters is what your wrist, forearm, and elbow are doing.
If you throw a splitter while pronating your wrist, then it shouldn't cause any more strain that a standard fastball.
It's true that Bruce Sutter was a splitballer and his career was cut short by injuries. However, those injuries didn't have anything to do with his throwing a split finger fastball. They had to do with his arm action.
In the same way, Fernando Valenzuela was a screwballer, but it wasn't throwing a screwball that caused him his problems.