No, there is probably no protocol, e.g. digital audio protocol, that the headset would receive over the analog cable. Also, it is usually not described if the analog audio will be used and sent to amplifier, or whether it needs to be digitized first. Chances are that the amplifier in the headset is class D and it can only work from digital signal (it is both a DAC and amplifier at the same time).

At least noise cancelling headsets usually have wildly different frequency response when you turn them on vs. when you connect analog to driver and drive it directly. I can't quickly find out the answer to this question: does the sound change if the headset is turned on vs. off? In the headsets I have owned that have had optional wired connection, the sound has always been absolutely terrible when powered off because manufacturer actually fully relies on DSP (or whatever amplifier circuit) to fix the frequency response of the driver.

Neutral -- meaning literally flat frequency response -- is also not how a speaker sounds in a room. There will be downward slope in treble, there will be boost in bass, and earlobes do their thing around 2-6 kHz at least as far as our eardrums are concerned. The point of these tuning targets is basically to mimic the tonality of a real speaker in a real room at a reasonable listening distance. So in a bizarre sense, if you have a reasonable tuning target, it will be v-shaped, but it also sounds similar to studio monitor's flat response in an actual listening room.

Then there are equal loudness contours to consider as ear's response is not flat either but depends on overall sound level. It is another v-shaped correction curve.

My opinion is that there is no single tuning target. As long as the response is somewhat like any of the various harman/soundguys etc. target curves, it is probably close to what it "should" be, especially given that there is not and can not be one single target as it all depends on assumptions used to derive it, and ultimately is up to individual's preferences and experiences, also.

I find it pointless to eq few dB boosts here and there, because there is no universal headphone audio truth. However, if something in the sound does bother you, it is probably best to fix that part. Yet, it can be due to any number of things, one possibility being that your individual preference for sound reproduction is slightly different from the manufacturer's approximation, e.g. maybe your main music listening room has bit different dimensions or your earlobes have slightly unusual shape, or whatever. It can be pretty much up to any random thing like that.