No the red legion ships are red
You see one in the mission where you wander before meeting Hawthorne
And unlikely Calus has actually been taking in the red legion troops as it said in the letter from the emperor mission on nessus
English
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Forgot what raid piece it was but Claus stats that he'll allow forgiveness to the red legion and let them join his ranks
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<Those were Carriers, totally different from Battlecruisers>