It makes a huge difference. In this video, 20 tanks kill 100 zerglings and lose only two tanks. With super-human micro, the results are... quite different. https://www.youtube.com/watch?v=IKVFZ28ybQs

Reaction time is the real difference in this video. A human can't react to the twitch of the siege tank cannon that happens just an instant before the shot lands, we treat it as something that happens instantly and thus, we can't react to it, not even with a single unit. If you apply a human reaction time to that AI, that behavior isn't possible anymore, even with perfect micro.

The SC community seriously obsesses over APM, but I'm not entirely sure if it's correlation or causation. I personally think it's overblown and became popular because it's one of the few things you can easily measure and compare between players.

Well, ignoring spam clicks, APM is a measure of the number of decisions that a player makes throughout the course of the game. You'd expect a player making more decisions to come out ahead in a game as fast paced and action oriented as Starcraft.

It's clearly correlation. A pro will still play at a high level with mouse only, or even keyboard only.

Example keyboard only game: https://youtu.be/cY0d2kHzrxY

it's largely overvalued, but you probably can't be a pro without at least ~150, slightly less than 3 actions per second, increasing as the game goes on.