This hypoethis is discussed in some depth in the article (search for "T cells"). TL;DR: Maybe. There is some evidence showing a link and other showing no link.

This hypoethis is discussed in some depth in the article (search for "T cells"). TL;DR: Maybe. There is some evidence showing a link and other showing no link. Some lab studies show T cells get a response., but other studies show no statistical link.