Short answer - No
If Your computer is using say 280 Watts and the PSU is 80% eff then, at the outlet, the power consumption is 350 Watts (a waste of 70 W). It does not matter if the PSU is a 500 W, or a 600 W. If all three at 80 % eff at that power level then both would waste the same 70 W.
The thing is not all PSUs are 80%, poor ones might be 70% eff wasting 120 Watts while a good PSU might be 85% eff and only waste 49.4 Watts.
The only other thing that comes in to play is that this eff. is not a set value. Say a PSU is rated at 80@ at 50% load, then it might only be 75% eff at say 20% load and then waste more. They same is true at max loads for some PSU,s
A good rule of thumb is to buy a PSU that is 50% to 100 % greater than what your computer really draws. Myself I go toward the double what My system draws at max load. The only problem with this is that at idle the load ratio gets close to the 20 to 25% level, But I have room to "grow"
Bottom Line - Get a GOOD Psu with a High eff rating.