If you are working against background Johnson noise at all frequencies, you have the same output snr as if you stayed on one frequency. You only gain against a jamming station in the case that they would have been on the same frequency as you would have been on without hopping and the other frequencies you hop over have no jamming.
My favorite example is hopping over the 100 channels in the AM brodacast band with a signal that is -6 dB relative to the 100 stations that occupy all 100 channels. You get a -6dB s/j output, you do not get a 20 dB processing gain and a 14 dB s/j output.