In ECDSA, the
R value in the signature is not the elliptic curve point $kG$, but instead only its x-coordinate, that is, an integer.
So, what do you mean by
R' + (C*G)? In particular, what do you mean by the operator
If you mean "the + is an integer modular addition, that is, we take the x-coordinate of the point $CG$, and then add it (modulo $n$) to $R'$", well, that'll give you an integer that's unrelated to $R$ (as $R$ and $R'$ are related as elliptic curve points not integers, and integer addition and elliptic curve operations have little to do with each other)
If you mean "the + is an elliptic curve addition, that is, we find one of the points with x-coordinate $R'$, and add it (using the elliptic curve addition operation) to the point $C\cdot G$), well, that'll work half the time; there are (usually) two elliptic curve points with x-coordinate $R'$, and it'll work if the one you pick just happens to be the original $R'$ point.