I have a cheap mic headset for voice chatting, but I hate the way my voice sounds through it. If I invested in a higher end gaming mic, would it improve the sound quality of my voice, or not?

Have you listened to how your voice sounds through other microphones and devices? It might just be you being unused to the difference between how you hear your voice when you speak and how it actually sounds. Not saying a different microphone won't improve it, but it's something to think about before shelling out for a new one.