Padding RSA with random number
The system proposed has no practical interest.


If $r$ is public, then it is easy to check a guess $\overline m$ of $m$ (compute $\overline m'=\overline m+r$, feed it to the RSA function, and compare the result to the actual ciphertext; it matches when $m=\overline m$). That possibility is a disaster in practice; e.g. if $m$ is a name on the class roll, or a credit card number, poof goes confidentiality.
If $r$ is secret and chosen randomly in $[0,n)$ for each message, then the system is safe and we can use $m'$ as the ciphertext, without needing RSA on top of that. That's in effect a One Time Pad.