Is your question related to the actual computation time of the FFT, or are you asking about how often the spectrum display gets updated?
The actual computation time is very short (I don't know off the top of my head, and it will vary from machine to machine). However, the longer the FFT window, the more data needs to be gathered, which means it will take longer before a valid spectrum is available. For example, if you sample at 48 kHz and perform a 48,000-point FFT, you will need to gather 1 whole second worth of data (48,000 samples) before the FFT can be computed, and you'll get a new spectrum every second (with 0% overlap). If you increase the overlap to 50%, you'll get a new spectrum every half a second.