Could the saliva from my his thumb sucking cause irritation when he rubs his eyes?

Possibly: The eyes are very sensitive, and almost anything can be an irritant. That being said, their own saliva would be unlikey to cause any serious problems.

Skin hates drool: Excess exposure to saliva can cause skin irritation. Thumbsuckers have excess saliva/drool on their thumbs which is known to irritate the skin on the thumb as well as around the mouth. Eye rubbing, however, is brief and mostly occurs with the back of a closed fist (not the thumb), so minimal contact with the saliva occurs. In theory, it could irritate the skin, but not likely.

Yes.: Thumb sucking is bad for many reasons. I havent heard of your issue, but it certainly makes sense that if your child rubs his eyes after taking his thumb out of his mouth that it could cause irritation.