Effect of Windowing Function on Autocorrelation Function
When you are using the FFT to get a measurement of the frequency content of a signal it is appropriate to window the data first to avoid distortions due to a rectangular cutoff.

That is not what you are doing with the FFT, though.  You are using the FFT and inverse FFT to efficiently calculate a correlation (an autocorrelation is just a special case of correlation).  Done properly with padding and such, the FFT will get you the exact same results that you would get by calculating the correlation in the time domain.  If you window, though, you will not get the same results.  In short, you should not window when you are using the FFT to calculate correlations or convolutions.