Relationship between $E_b/N_0$ and $\rm SNR$ with channel coding
The relationship between SNR and $E_b/N_0$ is independent of the code rate. Note that $E_b$ is the energy per data bit (not the coded bits), and $R_b$ is the (uncoded) data bit rate. As long as you keep using these values, you can use the formula given in your question. Of course, when going from an uncoded system to a coded system, the values of $E_b$ and $R_b$ will usually change, so the resulting SNR will generally be different.