no. it just means that the PSU is capable of delivering approximately 600w of power to the system. If the hardware you have plugged into it only pulls 350w then that's what the power supply will deliver.
To further divulge, it's always best to have a PSU capable of delivering around 1.5x - 2x the amount of power that the system actually needs so as to be safe that you don't put too much load on it and cause it go bottoms up as well as the closer you get to half the wattage of the PSU the better efficiency you get from it power wise so it'll be better for your components in that they get a cleaner delivery of energy.