Does 600 Watt PSU always draw 600 Watt, or only as needed?

If your PC is only using 200 watts, the actual draw will be a function of the efficiency of the power supply.  Typical power supplies range from around 65% efficient to around 90% (Seasonics and PC Power & Cooling).   If a power supply is 75% efficient, that means 75% of the energy it consumes is actually available => the rest is wasted.   So, for example, to provide 200 watts to the PC, it would use (200)/(0.75) = 267 watts.    There's no "continuous" rating on a power supply => how much it draws is a function of what the PC is demanding at the time [there is a "floor" -> a minimum amount the unit will use; but that's very low].

As Leew noted, however, the best way to know just what you're using is to measure it.   This is a very handy little gadget (I have several):  http://www.ambientweather.com/tdp4400.html

Wattage is a unit of power.. Just like horse power..
The rating you see is the max available from the power supply.
Just like the horse power -rating- for an engine.
An engine doesn't run at 100% capacity all the time. (It may never.)
It will provide the needed power and no more.
The same goes for your power supply.
It will only use what is needed to run the system.
It will only 'pull' from it's AC source (the wall plug) what is needed to run the system.
.

I can't locate the specs, but like a DC-to-AC converter, they can provide max power only so long... they are designed to provide constant power at an "up-to" point which is usually 10% either side of 50% of the total capacity.

Thanks all for thorough answers!