The answer is no, its not worth it. I have a Veloster Manual none turbo and wanted the same.
The cost would be into the thousands to get a Turbo and all the proper cooling and what not with it to get it right not to mention i think you have to get bigger manifold.
Also, the car is so light weight, even with my base model with a mod exhaust and intake it peels out at half the power at a stop. This is with S rated Pherelli tires i got. 500hp would probably snap the drive train. Save your money and get a newer slightly used V-Turbo. Im not a mechanic or knowledgable about Turbos specifically but my research shows that the cost and time to try it on a base model is better spent just getting a better version or car. The Veloster N for example. But thats a $32k car.
Also, you would have to pay to tune the cars ECM.