Well seeing as he had no real part in the creation of the world he wouldn't really be an Aedra, but he is most definitely a god. Even the Thalmor secretly recognize this.
1) Erase the Upstart Talos from the mythic. His presence fortifies the Wheel of the Convention, and binds our souls to this plane.
-http://www.imperial-library.info/content/forum-archives-michael-kirkbride
There's the one quest always cited whenever this topic comes up, http://www.uesp.net/wiki/Oblivion:Blood_of_the_Divines, where the blood of a Divine is needed to open the portal to Mankar's Paradise. You have to fetch Tiber Septim's armor and use his blood, which makes him a Divine.
There's also the NPC in Morrowind, Wulf, who gives us a cryptic message about the empire and a Lucky Coin, who other people in game speculate was an avatar of Talos himself. And of course receiving a blessing at his shrines. There's also already a precedent of mortals becoming gods via Mannimacro (a slightly different case) and the Necromancers Moon, and a PC in Oblivion who completed Shivering Isles.
Talos is certainly divine at this point, but technically he wouldn't be considered Aedric by the elves given that he was not among those that participated in Convention.
Not so much turning into an actual Daedra, necessarily. More like filling in for one, even taking on the aspect over time so by the time you meet him in TES5, he is Sheogorath, just not the original Sheogorath is all.
But yes, Talos is a Divine. Not an Aedra, but no less a Divine, which is why the Thalmor have to go to the lengths they do to weaken him.
There are many more gods than just the et'Ada. Apotheosis is secretly the entire point of every TES story. The Dwemer-by-way-of-Numidium, Mannimarco, Mankar Camoran, Dagoth Ur, ALMSIVI, Talos, the current incarnation of Sheogorath, and possibly Arkay are all gods or quasi-gods who began their lives as mere mortals (and whose primordial ancestors, of course, were gods themselves). It isn't a usurpation so much as a reclamation.
it also is quite clear the "Prophet" from Knights of the Nine is an Avatar of Talos