Essentialy, you do the same thing as an FFT for separation. A gaussian blur is a low-pass filter, and functionally the same as selecting all frequency component within a radius r of the DC component (assuming the DC component is in the center of the image). The radius r depends on the width of the gaussian kernel.

The only difference could be in computational time (might be that the FFT is faster) and will be different if you use a different kind of blurring (i.e. non-gaussian such as selecting a square region in the frequency domain).