Short answer: Not that significantly.
The power supply rating doesn't mean it uses that amount of power all the time, that's the maximum amount of power it's designed to deliver to the computer components. It won't supply more than the system should require, but because they aren't 100% efficient, the power draw will always be higher than what your system actually uses. If your computer needs 400W, a PSU that's 80% efficient will draw 500W.
Assuming this same computer runs 24/7, the waste itself will add 2.4 kWh/day to your electric bill.