Heh, I never had the patience to get good at Starcraft. I tried it, mainly played Toss (because I liked them thematically), but wasn't that great at it.
As for gaming in general, it certainly did help. But on a scale of 0 to 10, 0 being a complete klutz and 10 being a mechanics god, gaming helped me go from a 3 to a 5. When I broke Plat 2 and neared Diamond rank, I was a 5 fighting against 7s and 8s.
I knew that I could not hope to fight my enemies on mechanics alone, they would win that game every time. I started adjusting my playstyle to compensate for my mechanical deficit. For example, I started playing a lot of Janna. Janna is played as a defensive, lategame-minded support, and does not require the player to possess much in terms of laning mechanics. Other champions I got into were Udyr and Alistar, for similar reasons: they don't require much in terms of mechanical skill, and thus largely nullify the motor advantage my enemies have on me.
I also stayed far away from autoattackers (though I still played Kayle, because she's an attractive blonde and I like her in terms of her theme, appearance, and playstyle, and she was pretty overpowered back in the day lol).