yes, if circuit has DC/DC converter its efficiency drops down with rise voltage delta between input and output, so lower or higher voltage leads to higher heating. Step-up DC/DC also drain more high current from source with lower voltage. As result, undervoltage leads to higher heating and higher current flow and it can damage circuit components if it don't have protection.
Also, as mentioned above, MOSFET may not fully opened with undervoltage, so it leads to higher resistance and as result higher heating. So, it can be burned out if there is no protection.
Overvoltage also can damage circuit, because it can lead to higher current and higher temperature and can lead to breakdown of capacitors and semiconductor elements, such as transistors or diodes.
Note, that both - undervoltage and overvoltage can lead to higher temperature which causes transistor and capacitors ageing much faster. So, even if circuit is still works with undervoltage or overvoltage it still leads to shortened lifetime of circuit.
Overvoltage or undervoltage also can lead to a higher current in the inductors which can leads to inductor core saturation and as result high heating which can damage or melt inductor core or degrade its magnetic properties.