Given Nyquist, a non-infinite series of [non-trivial power of 2] nodes will do the job just fine.

Audio FFT/iFFT processing typically uses 512 or 1024 bins, although sometimes you can get away with fewer.

In practice, iFFT doesn't use discrete oscillators for resynthesis, because the whole point of iFFTs is to limit the amount of work you have to do.

But there's no reason in theory a limited number of oscillators couldn't do the job. (I've done resynthesis like this in SuperCollider when I wanted special effects that FFTs can't produce.)

I doubt WA would be fast enough on most machines, but it would probably be possible - if rather dumb - on powerful hardware.