Signing up is the first step, followed by updating to the relevant version - 15.36. Sign up, reboot, run the Microsoft AutoUpdate app, and see if you get the latest version offered as a download.
Signing up is not necessarily an automatic path to the Fast Ring, and MS's updates on the Fast Ring are not pushed simultaneously - read their TOS, it's in there. You may get updates pushed first, or last…
FWIW, I have Outlook synched to my "junk" Gmail account, and it works pretty much perfectly (labels, contacts, calendar). Not impressed enough to start using Gmail for anything important, tho'.