Technically, Capt. Charles Arthur Carroll's company, the "Pope Walker Guards," of Crawford County, was Company A of Col. DeRosey Carroll's regiment of cavalry. However, this assignment should be considered as purely administrative. From what I can tell from the limited records available, at least four of DeRosey Carroll's companies never actually served with the regiment, but instead operated independently under the direct command of the division commander, Brig. Gen. Nicholas Bartlett Pearce, as scouts and escorts.
So I guess the answer to your questions is "yes" and "yes." :-)