Sure, but the engine is going to drink fuel like crazy.
Plus, in the amount you're going to buy and install the supercharger onto the Vitz, you can sell the Vitz and get a fairly used RX8. There's no point in adding 40-50 horsepower in a car like that because it's not like you're putting it to the ground effectively. I guarantee you'll be spinning your wheels the entire time, snd the differential is so open that it's not even going to be the interesting kind of wheelspin.
My vote: don't go for a heavy mod like a supercharger. Just get an intake and a take off the catalytic converter. You'll feel the car is actually quicker. And don't even get an exhaust.... an automatic car with an exhaust sounds like you're hearing someone **** through a deaf ear.