Yes, but it's not just about going fast. Look, I was thinking of doing some more mods for my car, putting in a V8, for example. But then I discovered I'd need to stiffen the Chassis, update my tires more often, and then after that, get new brakes which would help me cope better with the engine's power.
All this would cost somewhere around 30k at least. 30k. Why not just get a brand new Mustang for that? It looks better, (Kias, Hondas, and Toyotas generally aren't styled as sporty cars) and it looks classier. Also, each car has a statetment about it, it can tell people about you. If you drive a modded out Kia, people are not only going to think you're weird, they're also going to think you're a major toolbox for spending so much money on such a shitty car.
Also, you can make a car go faster, but many cars are limited by their shape and the general aerodynamic properties. Cars that can go fast because of their engines are different then cars with loads of fast engines. Case in point: Lotus: It's engineered from the ground up to be incredibly agile, good for power tracks, but it's powerplant is 1.7L to 3.0L (max I think).
Again, you can spend lots of money on a shitty car, or you could spend that money on a new, sporty car, or (here's an idea) save money up, and buy an even more sporty car later.
Or skip cars altogether.