GPUs have single cycle sin/cos LUT implementations, so they should be good for this kind of thing - competitive with an FFT for a relatively small number of overtones.
But there are some technical issues. Older GPUs don't have full IEEE 754 floating point support, and compilers are optimised for graphics, not for audio, so you won't necessarily get the same output as you would from DSP code running on an x86.
If shader compilers included some audio-friendly tweaks and perhaps a standard audio API for co-processing, they could see a lot more use in music editing and synthesis.
But there are some technical issues. Older GPUs don't have full IEEE 754 floating point support, and compilers are optimised for graphics, not for audio, so you won't necessarily get the same output as you would from DSP code running on an x86.
If shader compilers included some audio-friendly tweaks and perhaps a standard audio API for co-processing, they could see a lot more use in music editing and synthesis.