I have about 20mV offset on my Realistic STA-64B which uses the typical quasi-complementary output stage. It doesn't really have an easy way to adjust it as far as I can tell. Anyway, suppose you have an 8 ohm impedance speaker that has a 2 ohm DC resistance. This 20mV offset would be 20mV*20mV/2 ohms = less than 1mW burned in the speaker. If the offset was instead 100mV, then 0.1*0.1/2 = 5mW of power dissipated in the speaker.
On the other hand, after I replaced a fried transistor, the quiescent/bias current draw on one of the channels shot up to 100mA. This calculates to more than 5 watts burn! The heatsink was getting warm after being powered up. After adjusting it closer to the 20mA mark that is suggested in the manual, it dropped the quiescent drain of that channel to a bit more than 1W, which saved 4 watts worth of power burn. Unfortunately (which could be fortunate) I don't have the ear to tell any difference in audio quality.
When idle (output at 0V+offset) the dissipation in the transistors are related to the quiescent/bias current. This has no bearing whether the speaker is connected or not (well, it does, slightly, but in engineering terms it's negligible.) Thus, that 5+ watts burn will be burned whether a speaker is connected or not.
I haven't checked how warm the heatsink gets now after reducing heating from ~7W (both channels total) to ~2.5W, but I figure that it won't get as warm anymore while quiet. Sort of trying to set up a Sankey diagram for it for curiosity's sake.
17W in (quiescent)
2.5W -> final output transistor bias
??W -> remainder of power amplifier draw
5W -> two pilot lamps (two burned out, so this should be ~10W)
5W (guess) -> waste by power transformer getting warm (eddy currents or slight saturation mismatch?)
??W -> radio receiver power
??W -> preamplifiers
??mW -> speaker offset power