No, his record is silent on the subject.

There was also a T. Lawrence listed as a Cook, Company B, 25th South Carolina Infantry who enlisted February 24, 1862 at Charleston, last recorded present at the Jul/Aug, 1863 muster

Here is an interesting discussion on the subject:

Were Cooks Enlisted in the Confederate Army?

https://deadconfederates.com/2011/07/17/were-cooks-enlisted-in-the-confederate-army/

…………….

There was in addition, a R. De. T. Lawrence, Private, Company B, 25th Regiment South Carolina Infantry, enlisted April 11, 1862 at Coles Island for the war, detached August 24, 1862 to the Signal Corps. as Signal Operator

Believe this was Robert deTreville Lawrence, and the two Cooks may have been among his slave population.
http://archon.kennesaw.edu/?p=collections/findingaid&id=47&q=&rootcontentid=5337

http://search.ancestry.com/cgi-bin/sse.dll?indiv=1&db=contentpegfamilyhistories&h=3850828&new=1

See also: Find A Grave Memorial# 76758540