So, the reason for Chaos Focus is actually because of Level 2+ Marked Chaos Psykers. Let me explain.
The Aspiring Sorcerer that comes with Rubric Space Marines is a Level 1, and he has the Mark of Tzeentch.
Based on the rules in the CSM codex, he MUST generate 1, and up to half from his god. There is no loophole here, if flat out says MUST ROLL AT LEAST ONE (page 70). It doesn't say 'must have'. It says must roll.
if you're rolling, you gain your Primaris. If you're rolling on Tzeentch, you gain's Tzeentch's Primaris. If you're level 1, then it's a non-issue; you gain your Primaris the same way a level 1 Loyalist would gain their Primaris.
When you're level 2, things get complicated. You MUST ROLL one power, but you CAN'T roll two powers, because it says 'may roll up to half'. This disqualifies you from maxing out and getting the Primaris. That's why Chaos Focus exists; so you always have the Primaris from the Mark table as a consolation prize.
TL:DR - No.
Addendum: I'm not speaking about Chaos Demons. I don't know how they work, honestly. I'm fairly certain, however, that the Chaos Focus only applies to MARK of chaos, so Demons don't qualify to get bonus powers (such as Horrors taking Daemonology and also getting the Tzeentch Primaris).
Addendum2: Just looked up the rule again. Yes, it looks like Horrors could get away with it. Demons can skip rolling on the god's powers, but Chaos Psychic Focus still gives it to them. THAT is the loophole, since it's meant to be one Psychic Focus or the other.
Last edited by Xabre; 03-19-16 at 02:21 PM.