You're the Grey Fox! You're under arrest for...for...for all kinds of things!
In all seriousness, if he can be as old as he was in Oblivion, I don't see a reason for him not to be in Skyrim. On the other hand, Would the PC of Oblivion becoming Guildmaster be canon?
What do you mean by how old he was? The gray cowl was passed down from master thief to master thief, the new head assuming the curse that came with it. To anyone else it seemed like the Gray Fox kept on living indefinatly, but that was only because they couldn't tell the difference between the old head and the new head of the guild. The curse whiped them from the history books, and they litterally became the Gray Fox. The CoC would be the first person who was allowed to continue with his normal life after taking the cowl.
At any rate, any action the CoC could take is technically Cannon. Some things, like if you slaughtered all possible people in Cyrodiil, aren't cannon simply because it's to far to the extreem to be writen in. So within reason, everything is possible. Hence why we get so little word about what happened to our past hero's. All we know is they went off somewhere never to be seen again.
The reason why the CoC won't be given credit for being the Archmage is the Mages guild doesn't exist anymore. The same with the Fighter's guild. The only person who would know the CoC was a thief would be the person he gave the cowl too, and they're in all likelyhood either dead or not talking. As for the DB listener...they don't seem like the type to keep records. And even if they did, the part of DB history the CoC was involved with was so...what's the word...bad, horrible, dark, bloody - that any recods would probably not be taken till long after the CoC had got the DB back on its feet.
And with the Empire in such a state, odds are documentation that the CoC was an Arena champion wouldn't exist. So in the end, enough has happened to allow Beth to not talk about it, and just let the player come up with their own Cannon ending when dealling with the guilds.