I am asking this, because I am having a hard time trying to check whether this is possible or not. According to this documentation, execution of plans should take a const pointer to the plan (which AFAIK is nearly meaningless in the C world, because you are totally safe (ahem) to change nested values...).
Maybe it could be possible, but I am completely unable to hack through the code of FFTW3 to find the answer by myself. I could not find a similar question, therefore, even if c2c/r2c/c2r really need to use &mut self, at least there is an issue explicitly discussing this.