Thank you for your informative, comtemporary newspaper articles providing more detail on this subject. Presuming the articles are accurate, this doubtless was a well-supplied company of infantry.
I had, of course, considered the Yankees as a possible source of ammunition for Co. C/4th Texas' Colt revolving rifles as you suggest. But considering that the U.S. government itself only purchased approximately 4,500 Colt revolving rifles for Union soldiers, it would seem that Confederate ordnance personnel would still have had a difficult time capturing enough Federal Colt revolving cartridges to meet Co. C/4th Texas' ammunition requirements.
If, however, the supply of "27,000 ball cartridges" (presumably conical ball) mentioned in the May 11, 1861 State Gazette article is accurate, then it is at least conceivable that Co. C's own supply of Colt revolving rifle cartridges may have been sufficient to allow at least a portion of its men to continue using the Colt rifles at Petersburg, as unlikely as that may seem at first blush.