Of course it can make a huge difference, but no matter how good your multitasking is, tanks still don't shoot up...
The point is, it's really easy to just outsmart an RTS AI once you figure out its tendencies. No matter how good it's multitasking is your own won't be bad enough that your flying units all of a sudden forget how to shoot down.
Having an intricate knowledge of counters and economy and timings(at least as far as starcraft goes) has always been superior to multitasking, but only to a point. There are things that you can take advantage of with near-perfect multitasking and control, but you need to actually know what to do with that control(and so far, no AIs do). A good example of what you can use AI for is in the article video demonstrating mutalisk/scourge control at a level which no human player would be able to accomplish. The only problem is that a human player would know that the AI is capable of that and just play around it.
An example would be some extremely mechanical starcraft players(NaDa, a korean progamer comes to mind) being able to just completely outdo their opponents with pure control and multitasking. The problem here though is that those players have such an immensely better understanding of the strategy and tactics of the game than a programmed AI can ever come close to even if it's not their strong suit(compared to other progamers who play more with smarts than raw hand speed). Their multitasking wasn't what won them games but rather a combination of their abilities. They still had far and away stronger decision making than your average player(or any kind of AI).