It will depend on the SMPS topology and its design.
Most forward (1 and 2 transistors), half and full bridge, need to rectify on a choke input filter, to run properly. If the current at the output is too low, the inductor runs dry and then it "disappears" from the circuit, and changes the mode of working of the SMPS. This minimum usually is between 10 and 20% of the full rated output current. So, unless the SMPS has an internal load, the light load or no load of a SMPS is disliking for it. It is said that the SMPS cycles. The logic starts the power stage, then the outputs cap`s are charged to a level higher than the normal output voltage, as a consequence that the indcutor doesn't work. The overvoltage protection stops the logic, leaving the caps to discharge tough the leak circuitry (Voltage sense, power led/relay, etc). When the voltage goes under the trip voltage, the logic starts it again and so on. So the SMPS starts and stops running entire cycles. If the SMPS is not prepare to this mode of operation, the power stage may blow due to continuously starting/stopping at audiofrequency ranges. Some IC's are designed for this job, and is usually called Burst mode. The difference between the two cases is that the burst mode IC's start with the soft start function, while standard IC's don't.
In the other hand, a slight overload is tolerable, and a 5% of overload is safe for them.
Some Class D amps may cause "Bus bumps" at lower frequencies, which is a devolution of the RF energy at the filter of the class D amp to the supply bus(es) via the output's MOSFETs causing the voltage to rise with no control. This also can affect the SMPS job.
