Having an FFT in Stan would be really cool!
One of the very cool applications of a FFT transform (and its inverse) is the possibility to calculate the convolution as a simple product of two functions in the transformed space. This is for example handy if one wants to get the difference distribution of two quantities; one simply FFT transforms the function, multiplies them and then takes the inverse of that product.
Long story short: If this is possible with what is planned then by all means it should be taken in consideration for the design. That would be quite useful I think.