It's likely to assume that one of the big reasons canonicity is such a problem is because of the way Star Trek is handled through licensing.
CBS owns the rights to shows, and Paramount to the movies. CBS was able to get a hold of the rights to the show when it was owned by the old Viacom, which also owned Paramount.
When Viacom split from CBS, and CBS became its own powerful entity, it took the rights to the shows. Paramount, along with Viacom, still owned the rights to the movies. Unfortunately, this created such a problem for the company (tried to find the name but can't find it) who was first licensed to bring forth a Star Trek MMO.
They talked about the difficulties keeping within canon, due to the politics behind the scenes. For instance, in order to get rights to model the Sovereign class, they needed approval from Paramount (as they owned the rights to the first piece of film that style ship was even seen in), for the Galaxy, they had to turn to CBS. The problem became even more complicated when it came to the Constitution class, as although the original was on TV (CBS), the refit was in Star Trek: The Motion Picture (Paramount), and there became a brief argument over who the rights for the ship belonged to, due to the fact that although they looked different, they were in fact still classified as the same ship.
Thankfully, the company who originally tried to make the MMO sold the rights to Cryptic, and the groundwork for issues such as these had already been laid. Cryptic also noted early on that the process was slow and arduous just to get rights for other ships and characters.
It's also likely to assume another big problem stems from the conflicts within the ownership of rights system. It's no secret the shows are canon, but with the inconsistencies the shows contain (such as the Hansens looking for the Borg with knowledge of them 10 years before the ENT-D encounters them), the problem, in theory could become "what are we willing to acknowledge and ignore?", and this would just be on the CBS side. Paramount's side would make the Borg as character/race even more complicated. We all know the Borg originated on The Next Generation, but First Contact was the first time we saw a Sphere, so the rights to the Borg as a race could be from CBS but the ships were split between the two. Also we see numerous Borg ships in red alerts that look exactly like V'ger's ship from The Motion Picture, and the Shatnerverse tells the story of how V'ger was, at least in part, a precursor of the Borg, and the rights for the design of that ship would come from Paramount. So with everything for just the Borg, in terms of STO, this could possibly mean that the origin of the Borg has already been explained through TMP to a certain degree, and further explained through the Shatnerverse, but since the Shatnerverse, according to Starterk.com/faq, is not considered canon.
In the sense of the game, the canonicity of the Borg's history could be ruled as canon specifically for the game and not the movies or shows, but could also very well be considered apocrypha and never fully explained, due to the various source material they chose from.
And, finally with every answer, there may be even more questions both CBS and Paramount are unable to answer or don't care to answer. If V'ger's ship is being used by the Borg, and the origination story from the Shatnerverse is being used, wouldn't that make, at least in part the Shatnerverse canon? Questions such as these would open up many other questions that have already been answered by the FaQ, but citing specifics would make those statements contradictory to what has already happened.
I think in the formal sense, STO cannot easily be classified as one or the other as far as canon is concerned. As with everything else Trek, though, it's hard to answer these questions, but in this specific, it may just be as simple as "maybe", since no one with the rights to the IP's wish to comment otherwise.