If the engine was designed with a turbo then it is *possible* you can damage SOME CARS by removing the turbo only and changing nothing else. Most likely it will be ok but just run like a POS.

CR will be too low. Intake ports will be too small. Exhaust ports too big. Valve Timing and ignition timing will also be off. It's not going to be a very good burn in the chamber either.

If you absolutely had to run it this way get the lowest octane gas you can find and advance the timing a bit to compensate.