The phrase let alone is used to emphasize that if other more significant or pressing things are not possible, a lesser thing certainly is not or cannot either which is exemplified in this context where Shaun and Mike won't even look at the each other hence speaking during dinner was out of question.
Consider the staetement "Shaun and Mike had not even looked at each other not to mention talk to one another during dinner.". Based on this statement, is "Shaun and mike had not even looked at each other let alone talk to one another during dinner." a true statement? Yes/no/unknown