No, because we're not one of their underlings. The Great Houses may have relied on mercenaries for some things, but most political intrigue was carried out in secret by trusted underlings belonging to their House. Or by hired assassins, in which case the person sent to carry out the assassination usually wouldn't even know who bought their services.
So because we do not start the game working for them, we can never work for them?
By that logic, since we do not start the game in the employ of the Dark Brotherhood, we can never be in the employ of the Dark Brotherhood.
Well, there are some bits that can be uncovered. Count Indarys's wife was murdered, and Count Indarys is the main suspect. Count Caro married the daughter of the Countess of Chorrol, who promptly tortures prisoners. Count Terentius seems to turn a blind eye towards skooma, since his own son is addicted. And Count Hassildor is secretly a vampire.
But the point remains that it's all just information without a use. That's the whole point of this thread, that Oblivion had lots of good plot hooks that were never acted on.
To dissuade the argument that the world has to have some plot hooks that aren't acted on, I believe this:
is more than adequate at pointing out the developers wanted to do political intrigue and properly sewed the seeds, but they ran out of time to reap them. And plot hooks that are contained within the boundaries of exploration are present yet not acted on, that's not a good thing. Akavir is a giant conglomeration of plot hooks that is currently not being acted on. But that's OK, because no game has Akavir within the boundaries of exploration. The extra-provincial plot hooks in the Pocket Guide to the Empire v3 are not used. But that's OK< because Oblivion does not have those extra provinces within the boundaries of exploration. Putting these plot hooks within the boundaries of exploration only to let them trail off to nothing is bad design and a hallmark of not properly budgeting time.
I don't think they'd try to openly take over Kvatch, for two reasons. First, it's be open rebellion. There's not yet enough assurance that the Legions won't be able to put them down to warrant it. Second, each city has it's own Count; if anything, they would try to get one of their relatives or offspring to be the new Count of Kvatch.
It depends on how you define openly taking over Kvatch. If we mean by military force, as you're arguing against, then I have to agree with you. However, there are a whole host of other ways to take over Kvatch. An appeal to the Elder Council that Kvatch needs overseeing by a neighboring benefactor until a successor can be properly chosen. Stirring up land disputes, or disputes over county resources like mines and the like. Allowing the Elder Council to put a figurehead Count in charge of Kvatch and then trying to control his administration by subterfuge and infiltration. Etc, etc, etc. And all the various pathways and avenues to attain those goals.