Ogryns being able to lead squads of their own kind is the result of the Biochemical Ogryn Neural Enhancement treatment, or the BONE treatment. This makes them more intelligent and capable enough to serve as sergeants called Bone'eads. Ogryns that seem to be smart enough for this are tested and, if they come out as positive, undergo this treatment. Exactly how much smarter they become is unclear.
As for their acceptance, Ogryns are not very smart but very loyal, will follow orders to the letter and have an unshakable faith in the Emperor, seeing all orders given to them as having come from His Imperial Majesty himself. Furthermore, they are very strong, carry big guns (or other weapons) and can rip enemies in half with their bare hands, making them very useful on the battlefield.
Not all elements within the Imperium like them, because they are abhumans. For example, the Monodominant faction within the Inquisition wants to exterminate all beings who are not pure humans, like Abhumans, mutants, Psykers, Navigators, Astropaths and Space Marines. But for the time being the contributions of the Ogryns seem to outweight the naysayers, and as such they remain under arms.
In Warhammer 40k the Imperium governments are responsible for giving their psyker to the Black Ship or the Inquisition, so it's mainly up to you. ;)
Each world will have it's own method. Don't forget that an untrained Psyker is far more dangerous than a trained one (even a Chaosian one); just look at the psychic phenomena table, or the next one: perils of the warp, it goes to just have some temperature drop to mass demon possession, with some funny thing like blood rain from all ceiling ;)
As long as your Psyker doesn't use his power, it'll will be very very unlikely that he will be found. Psykers are rare, and the ones with warp sense (Psyniscience test for free action) even rarer (except for the player, they always take warp sense ;) )
You can also have checkpoint at the spaceport, or before entering some sensible zones; these checkpoints may have a Psyker checking the visitors. But don't forget that they generally have better uses, if you have Psykers at checkpoint it must be very important.
But if your party does something out of the ordinary, something noticeable by a human, like all the food going sour around the Psyker, an inversion of gravity, someone hit by something invisible, or the roulette in the casino giving always the same winner, the chance that the populace are fleeing the zone screaming 'Psyker' is high.
And if there is reasonable suspicion of a Psyker being somewhere, the Inquisition will be there, and that is a risk.
Also, your group is not the only one trying to undermine the Imperium, so an Inquisitor may be there coincidentally. (The inquisition group may also be there for à false alert, and digging some heretic stuff.)
Best Answer
We don't know
I looked up in all of the published RPG books from Fantasy Flight Game that I had access to and found nothing neither confirming nor denying that:
So, the answer is: we don't know. We don't know exactly how the Sisters of Battle faith works, it could be the Emperor granting them powers, or it could be powers granted by having great faith in something, which the warps translates into their power. Saint Celestine could actually be a saint, but she could also be a propaganda scapegoat from the Inquisition (PS: I find that unlikely, they are terrible at organizing themselves to accomplish something like that).
Quoting Chapter Approved:
There is one distinction to make here though, which a lot of people are misguided about: What Saint Celestine is, and what the claimed Living Saints are, are two completely different things. Many of Saint Celestine powers have never been described as being used by other saints, especially her confirmed multiple resurrections, which is the thing that makes her most similar to demon princes, but also the ability to fly and survive in the void of space without any gear, the ability to resurrect her followers (Genevieve and Eleanor) and others (Guilliman), an ability also possessed by some demon princes.
There are a bunch of "saints" who are merely high members of the Ecclesiarchy, and not actually living saints. I will completely disregard those guys. As described under Saints on Dark Heresy: Blood of Martyrs (pg. 20):
As opposed to the description of Living Saints from the same book:
However, the actual distinction to make here is that saints are declared so after their death, and living saints were declared saints while they are (or were) alive.
A short list of known living saints:
We also have Saint Anais from Dawn of War, which is a copy+paste in every aspect of Celestine under a different name, and we don't know how canon the game is.
Finally, we also have the Belle of Lost Souls (Dark Heresy: Enemies Beyond, pg. 18), which may or may not be a saint that was corrupted by chaos.
That said, Saint Celestine is the only actual saint that has the abilities that make her sound like "a demon prince of the Emperor", if that is actually a thing. Not only that, but we have several "saints" who never came back from the dead.
The list of RPG books searched is: Dark Heresy CRB, Dark Heresy: Enemies Beyond, Dark Heresy: Enemies Without, Dark Heresy: Inquisitors Handbook, Dark Heresy: Blood of Martyrs, Black Crusade CRB (why not), Deathwatch CRB, Only War: CRB. Of course, I might be missing a book that mentions the saints, but I tried to look at all possible books that mentions followers of the Emperor in a way or another. And of course, I also searched the fan-made wikis for references.
The book about Celestine, the Living Saint
They have recently published a novel about Celestine. I have not read this book, but looking at the synopsis of the book:
I'm not sure what is this realm of suffering and torment, but seems like some kind of chaos dimension, maybe not related to the Emperor, or even any of the Chaos Gods, but certainly related to the Warp. It also sounds weirdly similar to how to orks get to manipulate reality due to their sheer faith that things will work the way they want them to work.
And a spoiler given by a random internet user:
Finally, quoting another guy from that same page: