Yes, but that “electrical engineer” would be making poor assumptions about the operation of the ear muffs.
There is a micro-second before the cutoff mechanism is activated.
During that period there are potentially damaging decibel levels.
The earmuffs that I happen to have do not operate by creating a counterphase signal. They are much simpler. They consist of:
This design does not have a delay, just because there is no cutoff switch and there is no need to process incoming audio in any way beyond clipping it. This is an inherently safe design. I can use them even without turning the amplifier on; then they just act as regular earmuffs. I need the amplifier only to hear external sounds; the amplifier has no effect on suppression of loud noise.
It is theoretically possible to have an active suppression scheme where earmuffs are not really attenuating much, but the speaker generates local audio that is in counterphase to what a nearby microphone receives. This is a very dangerous design - and I don't know of any electronic muffs that use it - because any touch of the microphone will produce a +150..+170 dBa right into your ears, without the ambient signal to counteract. This will be also very sensitive to the disbalance between what the microphone hears and what your ear hears, unless they are colocated (then you must be a cyborg :-)