Are there any cases of someone successfully turbocharging a 4th gen Prius?

I doubt that it would be achievable - economically. For a start, you'd void the warranty on both the engine and, I suspect the Hybrid drive-train. And - I suspect the computers managing both the engine and the Hybrid system would need massive overhaul - or they'd get utterly confused.

 

The Atkinson cycle ICE in the Prius actually releases some of the cylinder air/fuel charge back into the intake manifold on the compression stroke, so that won't work like it should if the intake manifold is pressurized. Plus, the ICE will periodically turn off with the vehicle continuing to move under full electric if the engine is warmed up to operating temperature, the hybrid battery has a suitable state of charge, and your foot is light on the accelerator. This would likely cause a very undesirable turbo lag when the ICE turns back on. As to the computer and ECU's, they are all designed for the present drivetrain configuration and I would imagine the programming is very proprietary.

 

A gentleman (I think the term is hoon) in Australia both supercharged, then turbocharged a gen 0 Prius. To his surprise, it charged the battery quicker. You may need to consider what you would do with more power if the software is not inclined to travel faster.

 

Try this and let us know how it works out!!

Universal 12V Electric Turbo Supercharger Kit Thrust Electric Turbocharger | eBay