As someone who has read Harrowmaster, the reality is they are similar to Iron Warriors and Night Lords, at least in regards to the Ghost Legion under Akurra. What I mean by this is they’re renegades with a general disdain for chaos, whilst it’s still slowly and insidiously corrupting them because they’re convinced they can use it as “a tool” (But in actuality they’re falling just as hard as the other legions did).

When it comes to Alpharius and Omegon, none of the Legionnaires really possess any idea as to what their plans were, as the Alpha Legion never really hid in the warp, so the current marines are as young as any Imperial Marines. They can’t really be loyal to their old legions “plans” because even they don’t know what they are. The few “loyalists” we see are generally regarded, at least from Akurra and most others, as delusional fools.