2x 160 can be done pretty easily. Only on same band/LO though. So, only for things like multipath.
4x 80 might be possible, but needs a lot more effort. It is up to 2 ports per icap engine and only one icap engine got coerced into writing to pooled sram. The other 2 could only do their designated regions that are limited to 16KB if I remember right. So continuous reception gets more complicated/precise.
Everything above is from me experimenting with HW. There is no official reference for this stuff. So I may have missed something, and some mentioned limitations may be workaroundable.
If you change your Fourier transform approach into a time domain convolution, then you can generate it sample by sample. White noise -> FIR filter, this is a pretty simple and direct algorithm as far as DSP goes. The wiki on pink noise mentions this. I've done the FIR filter approach to simulate 1/f phase noise.