No, it will not. Take the fastest typist in the world Sean Wrona, he is not a good Starcraft 2 player. I least I do not know him as such, and he types with 237 WPM on average, that is over 1185 APM.
But you need to have high APM to become one of the best Starcraft 2 players, most of them have more than 200 APM. But having high APM is not enough. I agree that it requires some finger training to be able to type very fast and to get high APM in Starcraft, but that is about it. You can get that kind of exercise in less than 1 month of regular touch typing training, because 200 APM == 40 WPM.
Having said that, touch typing is a good skill to have and you can probably translate some of it into Starcraft 2, but do not expect that if you train 20 minutes a day on a site like typingweb or typeracer you will automatically get into Masters league.
Here are the main differences between touch typing and Starcraft 2:
In touch typing you know what you have to write and you read N (e.g. 2) words ahead. You just need to correct yourself if you make a mistake. The faster you are the better you get.
In Starcraft you have a build order and a strategy, both require you to press certain key combinations at specific times. Pressing them too early or too late makes your build less optimal, you either end up queuing or not spending your resources fast enough. There is no highlighted text that shows you your next action. You have to memorize the build and check manually what the next important step is (eg. Build Barracks with next 150 minerals then another SCV, just before the current is finished...) This kind of checking or controlling what to do is the greatest part of APM in Macro.
Pushing buttons faster in Starcraft does not make you better, pressing them at the perfect timing does. At least that is true for Macro. Micro is a different problem.
In my opinion the next best thing to "touch typing" in Starcraft is the concept of the mental checklist: Look at these videos from Day9: #132 and #360. Both tell you how to invest your APM properly instead of punching random buttons on your keyboard.
Here is a short summary:
- Hotkey your Command Center to command group #1, Barracks to #5, Factories to #6.
- Cycle all the time through all of them and queue the next SCV, Marine, etc. just before the current one finishes
- Look regularly at your supply count
- Look regularly at the mini map
- Issue Micro commands in between