No to the main, numbered chapters.
TES is non-linear. TES has a main story, but it is never the only attraction.
New Vegas was a linear game cleverly disguised in a non-linear box. The side quests were almost exclusively dealing with the Main Quest in some way or another. That isn't TES. Bethesda is TES.
I don't think you actually played New Vegas all that much if thats honestly what you think about the game. Sure, a lot of quests were in fact tied into the main story of the game... but there were also dozens and dozens of side quests that had nothing to do with it (there was also gambling, crafting, snowglobe/Sunset cap collecting). In fact, there were probably more side quests in New Vegas that were un-related to the main story, then in Oblivion. New Vegas was no more linear (in fact, its main story was far less linear) then Morrowind/Oblivion. It just had much larger, and more dynamic main story that took up more of the game world.... that does not make it any more linear though.
Either way, just because Obsidian did something with one game... does not mean they will do the same thing with another game. In the unlikely event they were given a TES game to develop, I'm sure they would keep it far more in line with Bethesda's TES games. The well kept secret that no one on this forum wants to hear is that, aside from the game itself (the technical side) there is really nothing super amazing about the TES games that couldn't fairly easily be done by another developer. The stories are generally weak, the quests get repetitive, and the worlds (while usually graphically nice) are not the best designed/developed worlds in the gaming industry. Don't get me wrong, I enjoy the TES games... but given the engine and art assets to work with, most competent developers could put together just as good of game, if not better.
The REAL problem with Obsidian is that are incapable of making a game thats not horribly broken. For that reason alone I wouldn't want them developing a TES game... or another Fallout game for that matter.