I just got done reading the Blood of Kerensky trilogy for like the umpteenth time a couple months ago, and while I forget the exact details, I do remember that during the bits on Outreach, Romano Liao, that vindictive little witch, made it clear no Capellan unit would be sent to fight against the Clans, at least not if they were to be paired up with any FedCom units for fear they would be used as shields for the FedCom in order to weaken her realm further so that Hanse could complete then what he could not in the 4th Succession War.
It's never really clear whether Sun Tzu continued with his mothers policy after he inherited the Celestial Throne when Candace came a callin', bringing about some very personal retribution on her sister. Something tells me he kept as much of the CCAF within his realm as he could, and only contributed forces to Task Force Serpent and Operation Bulldog cause at that point he was still First Lord of the Reborn Star League, and only then because of the prestige it afforded his nation.