Me thinks your awnsering your own question,but to point out other relevant points.I'd think that would depend on the clan(insert name) and their rank,if Star Commodore is even there(probably is).The makeup of the parent Galaxy(TO&E) and having the Droper's to even assign' them(for this sake,we'll say they do).Because of the way the clans operate it wouldn't supprise me if said star Commodore had a bloodname,a decent codex and a Ristar(just a ex-sample here).He may even turn to the Star Col' and say "Then I suggest you strap yourself into your Mech' Star Colonel.Things are going to get hot before I can get you to your LZ.".Clan warriors tend to be egotisticall ;D
Now,even with the Star Col' in overall command of said ground cluster,the Star Commodore would still have the right to challenge,or change any orders that would put his ships in harms way and stopping him from completing his mission/orders,which I'm guessing would have come directly from a Galaxy commander,Star admiral or one of the Khan's themselves.Assets are limited in the clans as well as support units,so that would have been considered to.Hate to get your unit whipped out and have to face the Khan's,not to many second chances in the clans(if they even survived).
But hey,it's your table man,so do what ya wish.