Is it considered cannon? I remember talk at conventions that it was, but online arguments that it isn't.
Canon, not cannon.
The term "Star Trek canon" didn't start getting bandied about until the 80s, when Gene Roddenberry started to tire of fans at conventions demanding to know why certain aspects of tech and events from the licensed tie-ins weren't being observed by the TOS movies, while others seemingly were.
Roddenberry approved Bjo Trimble incorporating TAS into her first commercial version of the "ST Concordance", and DC Comics had added Arex and M'Ress into their post ST IV movie-era comics. By 1989, though, with TNG's popularity essentially assured, the licenses for all ST tie-ins were renegotiated and DC and Pocket were contractually stymied from referencing each other or TAS.
If you check the timing though, that was also the year that Filmation was wound down (with the rights for their entire back catalogue of TV series in a state of flux), DC Fontana and David Gerrold (both TAS luminaries) initiated legal proceedings over co-creatorship of TNG, and Larry Niven was shopping around his kzinti for a "Ringworld" RPG and a new series of novellas, "The Man-Kzin Wars".
So, a 1989 memo from GR's then-ST Office at Paramount respecified what was "canon". The Okudas were asked not to include TAS in the "ST Encyclopedia" or "ST Chronology", but they did get permission to reference Captain Robert April (using Roddenberry's own photo) and certain Vulcan aspects of the episode "Yesteryear".
As soon as GR passed away, though, in 1991, TAS aliens once again started turning up as references in the tie-ins, starting with the novelization of "Unification" (TNG).
So, for the most part, it's back in. But nothing official has ever come through from CBS or Paramount retracting the old memo.