Ultimately, it depends on the group, or more specifically its players. "Evil" groups are already a challenge as-is, as the risk of internal conflict is somewhat higher than in "good" groups (though this is an oversimplification, especially in 40k) ... and this is a concern that has been brought up even before BC was released. Yet, lo and behold, it worked out better than the sceptics were able to envision.
However, by basically programming PvP into the campaign as one of its core components, you are essentially forcing the issue, and at this point everything depends on how well the players can take their character - something in which they have (or should have) invested quite a bit of time, thought and thus even a degree of emotional attachment - getting killed. The worst case result would be that one player might end up sulking, even blaming another player. This kind of reaction might not only carry over to their new persona and their treatment of the killer's character, it might also taint the atmosphere at the table.
On the other hand, this challenge occurring very early in the game sort of "softens the blow", as losing the character now would be considerably easier to bear than if they had already spent months or even years playing and developing them. Also, you did say that you believe your players are able to separate IC and OOC. If this is truly so, then it might work out nicely, and it is an intrigueing idea. I would be tempted to forewarn the players about this aspect of the campaign, though, both to reduce the shock (unless this is specifically what you intend, re: "brutal nature"), and because a lot of groups have a tendency to coordinate character creation, by collectively discussing party roles and maximise their synergy, which in this case would be a disadvantage and might even predetermine the end result simply by looking at the character sheets.
Which leads into the next problem, the one already raised by Calgor. Is this challenge solely a physical confrontation, or can it be influenced/manipulated by wit and intrigue, such as characters making deals with other PCs and NPCs, setting traps, and generally sabotaging a "fair" fight behind the scenes? If yes, things might get very interesting, though I reckon this approach would also require a lot of one-on-one time by the GM. Also, what about characters who are smart enough to know they stand no chance against the likely victor, and who might thus want to focus their efforts on getting on this prospective champion's good side in order to become their minion?
Especially if you have both humans and CSM supposed to compete against one another. And even moreso when neither has weapons or armour. I mean, if they are fist-fighting, a human's only hope (barring psychic powers) would be Zealous Hatred, whereas the CSM does not even need to roll for damage to inflict Wound damage. On the other hand, I guess anyone with psychic powers would have a ridiculously easy time, as their powers essentially replace ranged weapons, and the lack of armour makes them even more potent...
What did you have in mind for these challenges, exactly?
Not sure about having everyone come up with 3 characters, by the way. This depends a lot on the individual players again, but there's a risk that they would end up less developed than if they were to focus their attention on a single personality. That being said, this could actually be a boon in that it reduces personal attachment and keeps potential for further development for the ones that actually survive. What is important is that the player actually ends up having fun with whatever remains of their ideas. Being forced into playing one's 3rd choice could be considered a bit of a blow.
How about having everyone roll a CSM and have those compete against one another? The survivor gets to be the Champion, and the other players can roll up whatever character they like. That might be the easiest solution, and it allows you to keep the trials a bit more balanced, and thus challenging/exciting.