\copyright symbol, in the default OT1 encoding, is constructed (and actually uses the OMS encoding).
The ‘c’ is shifted by a length tailored on the Computer Modern Roman font, but it's easy to fix this so the character is actually placed in a symmetric fashion inside the circle.
\char 13 % "0D
helvet should be loaded with the
scaled option, or the letters will be much higher than those in the Roman font.
From the comparison it's still clear that lowercase letters in Helvetica are still bigger than those in the Roman font, but with
\vcenter it's unimportant; of course I exploit the fact that the big circle is centered with respect to the math axis.
If you load the
textcomp package, the symbol will not be constructed, but in the Helvetica font it will be smaller and raised above the baseline.