Well I was interested in Coups as a kid particularly because my parents went through two. Anyway what determines whether a coup would be successful or not or whether it would even be the right tactic to use would be the structure of the village not just the physical structure and geography but the overall mentality in the village and the way people act and possibly most importantly how easy it would be to control the way information is spread.
Based on the way things appeared to have been at that point in time and the way in which Kishi presented the village to us I think a coup would have worked perfectly in Konoha. In contrast I would think that attempting a coup in a village like the sand would be and utterly foolish idea.
The political structure of Konoha is what I think would make a coup successful in that the second tier you mentioned didn't exist. Added to that is the fact that the majority of konoha were non-combatants and therefore don't need to be accounted for because not only were they ignorant of everything around them but as the general populace tends to be they would much rather just remain absorbed in their own lives and not have to deal with or think about any political struggles or the potential consequences of those things. Not only that put it has been proven that these people can be easily manipulated given the right information or misinformation, this situation or the situation with Naruto, I think are perfect examples of this. Anyway it would be simple enough to say that those guys are inconsequential.
The next thing would be your average shinobi this would be where the potential problem lies because the actions of these guys would be hard to control and to predict.Naturally I'm sure a small portion of them would willingly accept the Uchihas if only for the sake of self preservation. I can't really say what would happen with this group but I think it would be safe enough to assume that the majority of these guys would unite under one leader or possibly a group of people possibly anbu and attempt to put down the clan. These guys would be the X factor and would be the ones who would really decide the outcome if indeed something were to happen. How they would react would depend on how the next group is dealt with.
Now we get to the root of the matter, the anbu. This is were things get dicey. The other groups would be easy enough to control depending on how the anbu are dealt with but there in lies the problem. The anbu of course would be the most predictable group but would be the most difficult to deal with. Assuming the hokage and the elders are dealt with and that there was no second tier these guys would automatically assume the role and since they were fiercely loyal in the first place would of course intend to strike at the Uchihas. There are many ways this could go but my reasoning would be that after the initial shock passes a group of anbu would immediately launch a counter attack which the Uchihas en mass should be able to repel.
Then by my rationale what the Uchihas would have to do would be to essentially use the first group as hostages and convince the anbu that not attacking is in the best interest of the village and that attacking would carry a costly price. The anbu too would have to consider the fact that even if they did succeed not only would the leaf village be without its leaders (the third, danzou and the elders) but without the Uchiha clan as well and the village of course would be severely damaged leaving it ripe for the plucking.
This theory of mine of course is based on me assuming alot of things I just don't know and even so the Uchihas would have to have a lot of things in place before this coup was even attempted. For example the Uchihas would have to have outside support because regardless of whether they succeeded or not it would have all been for nothing if there wasn't other countries or villages supporting them. This I think is one of the reasons the Uchihas didn't strike before because if it is as Madara said and the Uchihas were subject to the will of the Senju since the very beginning and even more so after the second Kyuubi attack then they would have definitely made a move earlier. As you said Yuki, Uchihas or not, there would be no way the Uchihas would have been able to make a move against the Sengu unless they had outside help.
Another important thing which they would have needed outside help with is controlling the trade and resources going in and out of Konoha for obvious reasons. Anyway that is my wild theory on why I think a coup could've worked. Beyond all the complicated details the simple fact that the village was run by four people and those four purposely withheld information from or misinformed the general public even the ninjas working directly under them would have created enough of an opening for a coup to work.