Help can cubital tunnel syndrome/ulnar nerve damage cause twitching muscles?

Yes: It can in the distribution of the ulnar nerve but not in other places.

Yes to your question: Damage to any nerve that supplies a muscle may cause twitching. When the ulnar nerve is damaged, twitching may occur along the medial forearm, and many muscles that move the fingers - such as the muscles that move the fingers apart and together and the muscles that help the fingers curl and grip. http://www.neurocuro.com/peripheral-nerve-entrapment/