You will be able to see it visibly really early, the issue will be that individual mistakes or limitations will limit the result of it. I.e the extremely high pace of passing may very well become sluggish instead as a poor touch or a need for one touch extra would ruin the tempo for the entire team.
I find the latter half of your point important. I do have a hunch that our attacking players will flourish under Van Gaal. Even under Fergie, our counterattack play was always excellent. Noted for brilliant one touch movement, we'd smash past our opponents over the years. It was when Ronaldo was last around we saw the full effect of one-touch movement in our team. Since then, we've not done that. In Fergie's final year, we didn't counterattack much, rather we played with a solid number 9 running the show - RVP.
The likes Of Rooney, Mata, Kagawa, RVP and even Herrera will relish Van Gaal's one touch quick play. W'e've seen all of them play that way for their clubs at times and they've look very comfortable doing it.
Our midfield is the cause for worry as most people know. We don't have a man who initiates those movements from the back. Carrick did that three years ago to tremendous effect and he was our most important player at that time. Cleverley, believe it or not, had that one touch movement and looked really promising, until Kevin Nolan smashed into his legs from behind in that match against Bolton a couple years ago. Clevs hasn't looked the same player since. Herrera may well be that person, but he'll need help.
Another problem we might face is the extreme lack of technical/tactical prowess down the wings. Nani is far too inconsistent and tactically weak. Valencia may be tactically better but he lacks the technical qualities of a Robben or Depay as we witnessed in the WC. Let's not even talk about Ashley Young. I don't rate him one bit. He's had his moments. Especially in his first season. The moment the shit hit the fan he's looked lost on the pitch more times than not. He's not a very intelligent player, but you could argue that he can be effective on his day.
Smalling is a decent ball playing defender and even better is Johnny Evans! I don't think people give enough credit to his passing. He does all the things De Vrij does for the Dutch and is a better defender over all. Jones is a jack of all trades, yet his ball retention under pressure is questionable. Luke Shaw is infinitely better with the ball and he's shown that with Southampton time and time again over the past two years. in the PL. I'm not talking about effectiveness, rather his ability to play intelligently from the back. Rafael is even better with the ball at his feet and I think he'll really flourish under Van Gaal. Unlike the typical Brazilian player, Rafael doesn't mind being schooled or yelled at. He's all heart and we've seen that over the years. Aggression is a quality Van Gaal will develop in him.
Finally De Gea. LVG could not ask for a better player at the post to initiate his style of play. At ease on the ball and temperamentally excellent. LVG promoted VDS to greatness and De Gea is in the same mould, except with even better distribution at his grasp.
These are the key areas LVG will have to work on. It's also how his philosophy could work (with the right players!)
Now all we need is a Vidal in the middle of the park to dominate that space and bring "stability" to the team. Add a top class winger to the mix and winning the league is no longer a joke. We're going to be alright.