Doing what you asked would make no difference in that regard.Because as it is, I think it should be rcd protected? not sure.
If you meant an RCD FCU then, no that is not the way to do it. One of them behind a WM could be most inconvenient.
If you can change the MCB for an RCBO (if available for your Consumer Unit), or move the circuit to an RCCB if there is one, then you can do that if you want to.
If they are not available then it is likely it was installed before required so I wouldn't bother, but up to you.