Changing tire size will effect with mileage

Well it might change your "apparent" mileage that is displayed by the onboard computer .....and might make the actual mileage a bit worse as those will likely have more rolling resistance.

I hope you realize that you will have to buy different WHEELS......as 17 inch tires won't fit on your 15 inch wheels.
Then, the wider tires might rub something when turning sharply.

Your idea of making a C more "sporty" made me grin.

 

I don’t think you should do this. I believe it will make the tire speed sensor think something is wrong and throw codes.

 

1. Likely, but not guaranteed.
2. 45 series is pretty low. More prone to blowouts & rim breakage if you hit a large pothole. 195/45R17 is not a popular size, this could lead to a lot of waiting for replacements if something happens. This size will require wider rims than stock, and that means you might have a problem with rubbing- almost impossible to predict without a test fit.