I wouldn't know...
If that were to be done, the head would be scanned with a 3D scanner, and added to the background, either like you do in two parts, or one single piece.
The circluar plaque would be a matter of making the base, creating a convex center, and creating the text. That would take about 5 minutes to do. If the text was hand drawn, it would take an additonal 15-30 minutes, for a total of approximately 35 minutes. Text in a cove, curved surface, flat surface, makes no difference.
The final output would not be much different than hand carved, with the exception of the obvious hand tooled marks, which can added after the fact.
The CNC can produce some exceptional work, check out my web site of the city seals. The richmond was created entirely with vectors that were then modeled within the 3D program. This is in no way intended to say it's better than hand carved, just different. CNC work, in the right hands can produce excellent work too.
Danny