You're confusing two different things. Ye as a plural pronoun is a bone fide archaic English word, ultimately sharing an etymology with the still-extant "you". "Ye" as an article ("Ye olde...") has the history you reference, where the y comes from a stand-in for a thorn (th), and so was not supposed to be pronounced as "yee". But ye as a pronoun (by far the most common usage, I think, and the usage in the poem) is just a normal word and doesn't share that history.