Technically, you need to change the ICC profile in the OS when you change any display setting. Even brightness. That is, of course, if your ICC profile is that accurate and you pursue colour accuracy. This is why professional displays usually have an option to lock all controls once calibration/profiling is done.
I don't know specifically your Asus, but normally displays that offer sRGB emulation do convert input colours, just like a PC during colour proofing would. So an input (255,0,0) could produce a less saturated red; say (244,4,1) internally.
A few potential conversion problems could arise in this mode.
- What base are we starting from, i.e. what are the native colours, how red is the native (255,0,0)? This is the standard problem of profiling, and it is still applicable.
- Professional displays which have built-in LUTs and know their own profile (they come with specialised software which manipulates the display directly instead of asking the video card to do it) can translate precisely: from the measured native colours to the known/standard sRGB.
- Consumer displays presumably base off the factory calibration. In this case sRGB mode would drift together with native colours over time. That's (sort of) OK because this would happen with the "normal" display, and that's what this mode is emulating.
- What is the algorithm, the so called rendering intent? This is usually trivial because the target colour space (sRGB) is narrower and is wholly contained in the native space of a wide-gamut display. Most trickery of colour conversion happen when you need to do the opposite: cram a wider-gamut image to a narrower-gamut display/print. In our task, the display mainly needs to ensure that (255,0,0) produced a red that is as close as possible to the specified sRGB primary red, and similarly for the other primaries. Other colours can be linearly interpolated between these.
- What is precision of conversion? Many consumer displays are entirely 8-bit (even if they accept 10-bit input), which inevitably means that the narrower sRGB space will have fewer steps of each colour, and thus fewer than 16M colours. But for such displays, it would happen no matter how you'd try to emulate sRGB. Better displays have higher-precision processing.
I'm not aware of any standard for the display to tell back to the OS that it changed some settings, including the sRGB emulation. So if you switched to this mode using display controls, you need to tell the OS this fact by changing the current ICC profile. Ideally, you would profile each mode and have an ICC file for each occasion (and update them regularly). Yes, this is somewhat burdensome and prone to errors, which can be disastrous if you forget to change the profile and start doing colour-critical work.
It would be technically possible for a display manufacturer to provide a software tool that would manipulate display settings from the computer. It could then simultaneously change the OS profile and the display mode. I don't know if Asus has something like this.
The typical use (esp. home use) of sRGB emulation mode is to work with non-colour-managed software/devices, particularly video. Which is usually a non-colour-critical task to begin with. If you have a piece of software that bypasses the OS colour management and spits out uncorrected image (and you know that!), then you don't need to change the OS settings. If the source for such software is the standard sRGB or a related Rec.709 (usually assumed), then trying to display it in native display colours will result in oversaturated (and slightly colour-shifted) image. In that case you can just switch the display to sRGB emulation. Then this image will show more or less correctly, while all the colour-managed applications will look desaturated.
Also, note that good displays keep settings specific for each input. If you have two sources connected to the display (say, a PC and a video player, or two PCs), one input can often be set to sRGB and another to native. This is convenient, but you need to manage all that and know what's happening in each moment. Using several modes is always a responsibility, just like working with multiple units is.