No, JPEG does not employ perceptual color similarity detection. The banding which one observes is the result of severe quantization of 8x8 pixel blocks (DCT coefficients actually). this results in only the DC coefficient being retain for storage in the file data. hence each 8x8 block assumes the average color data with no details. this is the same effect in video coding (MPEG, H.264), in which to some extend, loop filtering (deblocking) is used to smooth out the "banding" artifacts.
additionally, if your image contains grain noise or shot noise, it is highly recommended that you save in highest (ONLY) quality setting. other wise, the same quantization process will try to remove your noise (high frequency) and result in "ringing" artifacts.
Otherwise, attempt to denoise your image first before saving in lower quality settings.