Error Propagation through an IFFT
Maybe it helps you to note that the FFT or IFFT with length $N$ can be realized by multiplication with the Fourier matrix $F$, or its conjugate transpose divided by $N$ respectively.

If you have the covariance matrix $\Sigma$ of your signal in frequency domain, the covariance matrix of the signal after IFFT (or multiplication with $F^H/N$) is then given by the usual way to compute the covariance matrix of a linear transform, i.e.

$$\Sigma' = 1/N^2 \; F^H \Sigma F$$

Note the prefactor $1/N^2$ is just because the IFFT is given by $F^H / N$.