Are the ratings on a bench supply absolute or do they imply total power output?
A bench supply rating will usually apply to current output. Although many of the components inside the device may be rated for a higher current at a lower voltage, the current limiting circuitry will kick in based on current. An example is below:



The supply will clip the output in the event of overcurrent. This is usually true with fixed supplies as well as those that have adjustable current limiting (Topward Triple supplies are a great example of this). The voltage will not be able to rise above that which causes the output to exceed the current limit.

Again, this is just typical. I'm sure you will find some cheap supplies that don't protect themselves and just burn out.

edit: for supplies that don't have current limiting, the AC/DC circuitry will most likely begin to ripple because the capacitors aren't rated for that high current output. Your signal will gradually degrade and probably lead to failure.