There might be more buckets, but the number of waves would be the same. I could be wrong, but I would assume that it takes a certain number of cycles at a certain frequency for something to determine the pitch (or frequency) of the sound. No matter how many sample you have of that sound, it will still be the same number of cycles long.
There is a certain minimum time period involved. That is why you can't reduce the latency usefully below a certain point---the buffer has to hold a reasonable portion of the wave. That's also why they provide a separate pitch correction algorithm for bass instruments. That's not what I'm talking about, though. You have to start with the assumption that you have enough of a wave for the fundamental to be the strongest FFT bucket anyway or pitch correction will flat out fail.... Well, more accurately, it will fluctuate wildly, and a properly behaving pitch correction algorithm will treat it as being random noise rather than a correctable pitch....
In an FFT, you transform a signal from the temporal domain to the frequency domain. So instead of expressing the signal as a series of voltages at discrete points in time, you are expressing the same values as the sum of sine waves at various frequencies at various volumes (positive or negative). You can then determine the fundamental frequency by looking for the largest value (basically) and seeing which bucket it is in, but that only gets you the frequency accurate to +/- the width of the bucket, which is determined by the number of buckets.
To get the real pitch, you have to take the largest value and the value to either side, then apply curve matching to find the exact peak. That peak might be... say 7/8ths the way between two adjacent buckets. If you start out with twice the accuracy, you can now find the peak with greater accuracy because you started with twice as many values in the frequency domain.
Incidentally, this also applies to algorithms that do pitch detection in the time domain. The way you do that is to (usually filter the heck out of the signal and then) try to count zero crossings or peaks and try to average out those values in a sensible way. There are many algorithms for doing this, and in every case, you need to calculate the crossing or the peak as accurately as possible, which means you get better accuracy with more points.