Is filtering necessary if I'm not downsampling?
Filtering is not necessary as it would only effect those frequency bins outside of the passband.

However, depending on how small your passband is, you could potentially save yourelf a lot of FFT processing by low-pass filtering and then downsampling before your perform your FFT.  For example, if you downsample by 4, the resulting FFT could be 4 times shorter and still have the same frequency resolution.