[Heroka Vendile]

Quite so Rhaalidor, though you would probably also play an excommunicated chapter with the CSM list as well, just without any marks or chaos-specific units like defilers, oblitoraters, daemons, noise marines, etc.
An example of such would be the Flaming Falcons from the cursed founding, who while they are reviled and hunted down by the Inquisition for complete eradication, they still for the most part, or at least to begin with, follow and worship the Emperor.