Yes, I've verified that the correct signature has been selected.
I've also tried another account on the same device (tested on a Chromebook with student's account and another one).
I couldn't find anything in the account settings that would control signature formatting. Text comes through, but no hyperlinks. We tried both Namecoach's button (small graphic with HTML) and a standard hyperlink. It looks fine in the settings view, but after saving, it doesn't work in a new Gmail.