Is it possible to read the exhaust gas pressure of a turbo car with an Arduino, and then control an electric motor based on the pressure?
Yes, I don't see why it wouldn't be possible.
You would need a sturdy barometer, preferably a digital I2C one because they are typically more accurate. I recently bought this one to measure altitude: BMP180 Barometric Pressure/Temperature/Altitude Sensor- 5V ready.
Be careful about the temperature that the sensor will have to deal with, its maximum temperature is 85°C (185°F).
The motor, I'm assuming, would be fairly large so you would need a beefy motor driver that uses a 5 volt logic level, maybe like this one: L298 Dual H-Bridge Motor Driver.
This is a fairly difficult project, I'd say mostly because of the difficulty you would have mounting the barometer and motor. Never the less, it still is possible.
You might want to look at https://github.com/designer2k2/multidisplay they're doing exhaust gas pressure monitoring and a number of other things.