There's a chance that one of the PCs is going to be possessed by a Slaaneshi daemon, which is currently bound to an object for the purposes of corrupting the local nobility and helping the world fall to chaos.

Since possessing an Acolyte of the Inquisition could be extremely convenient for this purpose, can such a Daemon avoid altering its host and mimic their normal behavior for infiltration purposes? Or more specifically, are there any rules that specifically contradict this (as a GM I can say this will work, but I'm not going to go against canon for the purposes of this).

On a similar vein, are there any examples of such a daemon altering the host body for the purposes of disguise and/or infiltration? Do possessing daemons have this level of control, and if so how long does the process take?

Depending on how mighty the daemon is I would definitely say 'yes'. I think somewhere in enemy beyond it is even mentioned that there are daemons in human form pulling strings in the Askellon sector ...

Yeah, there's multiple instances of Daemonic influence on folks concealing itself on the surface while doing its diabolic work. Instead of rolling up random mutations, pick and choose the discreet ones; better yet, come up with a few of their own (something like giving the PC Unnatural Fellowship when no-one is looking would not be amiss in my book).

The rules for daemonhosts allows a chance for them to look completely normal (minus the wards, chains, and other bindings of course), and Black Crusade has a Gift of the Gods called 'Illusion of Normality', which hides all mutations. Given these rules, it makes sense there'd be non-mutated possessed, or ones who have masked their mutations. Hell, DH1 had daemon familiars who could take the form of a normal human, so there's even more evidence for you to go off of.

Of course, I'd say it also depends on the daemon the type of mutations that do or don't occur. After a certain time, the host of a Nurgle daemon might take on a sickly appearance, regardless of whether or not the possessing daemon means to do so. A Slaaneshi daemon might not be able to help making themselves more attractive after a time if they possess an ugly host, or they may alter less apparent things... like what's inside the pants of their newly possessed victim

As to how long alterations actually take, I don't think there are rules for it, and mutations in fluff are wildly variable with their onset, so I'd say use your best judgment as a GM.

As much as it would benefit the plans of a daemon to be able to walk amongst humans without notice, I would argue that the answer is no, barring the examples given by Crow Eye etc... And for two separate reasons:

The essence of a daemon is totally different to the essence of a human. The human body simply cannot encompass the daemon “as is”. The wrongness of it will show in the body by way of erupting mutations as the body slowly fails to contain the daemon. Which allows a GM a lot of fun as the daemonhost tries desperately to hide this wrongness…..

The second reason IMO would be the vainness of a daemon. They likely see themselves as perfect beings, an unholy physical expression of their own desires and that of their ultimate master. Being wrapped in the trappings of a mere human must be disconcerting (even if it allows them to further their plans). Likely, the daemon can’t help himself from tinkering with the human form by slowly improving it because daemons have a different frame of reference as to what is useful and desirable.…..A violent daemon might harden the skin or improve strength with improbable muscles, a slaaneshi daemon might turn the physical attractiveness of his host to 11, or perhaps improve it by turning it into some kind of freaky she-male.