I had the same scenario in mind, but still if the CF drifts wide he doesn't drag anybody because the fullback can just mark him without the risk of being exposed since Neymar & Messi are already in the center. So the most effective way to do this would be to have N&M play out wide, this way the fullbacks are already occupied so the CB has no choice but to track the CF leaving space for the winger on the opposite side to get into or for the other winger to cut in. But as I said, that's no different from Messi old position and there's a reason why he no longer plays there anymore.
No, the fullback cannot completely key on the CF because he has to cover the wing from the attack of our fullbacks bombing up the wing to provide width. The CF does not need to move all the way out to the wing, just run towards the edge of the box, that still keeps him in striking distances thus requiring at least 1 CB to stay close, but still provides space by unclogging the middle.
Look at this goal. Notice how when Messi receives the ball, he has 1 midfielder and 1 centerback on him. Higuain drops a little back to serve as a dump off, collects marks, the unloads back to Messi and proceeds to make a run, effectively dragging the CB that originally came out to mark Messi.
The same point I just made also applies here. The CF doesn't drag anyone with him if all your attacker are in the center, because the fullback can just take care of that. Now since you can't play with 12 players on the pitch playing Fabregas means sacrificing either Xavi or Iniesta, so you end up loosing something. The other point to consider is that if N&M are playing behind a CF then they have to pass 2 lines of defense instead of just 1 and here the CF is not much help in creating space because he doesn't drag anybody.
Again, you cannot defend a CF with 1 fullback, that is a recipe for disaster because you can just bomb your own fullback forward and create a 2v1 missmatch. If the CF moves to the side of the box, he will inevitable drag a marker with him, and since the CF is playing in the middle constantly, CBs are programmed to cover CF, one of them will always attempt to stay close to the CF. This is how CFs and CBs operate.
As to the other part, playing Cesc, Iniesta and Xavi together with Messi and Neymar up front is not a productive lineup and would inevitably push Cesc to the center as a false 9, and both Messi and Neymar to the wings. It's always going to be an either or scenario with Cesc and Iniesta, regardless of bringing a CF or not.
The most effective way for a CF to buy space for N&M would be to have N&M play out wide; making N&M less effective. In the Valencia clip, Neymar was in the CF position; so what he & Messi have to offer whether they're playing a CF or in the hole is much more than what a traditional CF/Winger/AM can offer and that's why Messi was moved to the center even though he could've stayed on the right to play behind a CF while given more freedom. The reason being that with a CF, M&N movement become much more predictable because they have to track the CF's movement whereas without a CF they have more freedom in terms of space (yes, because there's only 2 players) and movement making them more unpredictable and hence more effective.
I tell you again, playing a CF does not require pushing them to the wings. This is a fallacy. Argentina play with not one, but 2 forwards in Higuain and Aguero, yet Messi does not play in the wings.
In the Valencia video Neymar was not acting as a CF. He initiated the play from the wing and just stayed centrally. He did not drag any marks, in fact, it was Messi who dragged the marks from Neymar from his deeper position after the pass. If Messi had a CF to his right when Neymar made that run from the wing, the CB would not have rushed to mark Messi after the pass from Iniesta, and Messi would have had a lot of freedom to dribble on, or lay off a pass.
