Hi Len,
indeed, you will see a difference on your SA, but it is also very informative to look at the demodulator output signal of vanilla type receiver with a o-scope, too. Watch out for clipped waveform, and never underestimate the good old eye diagram in the case ok FSK!
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Best results when your receiver is very good aligned, e.g. the carrier signal is smack dab on the true center frequency of your IF filter. In case of FSK one should always consider a group delay optimized IF filter, i think there was a D suffix...
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In case the remote transmitter is cooperative you can even measure deviation remotely:
If deviation divided by modulation frequency is 2.4, the carrier will be suppressed (first carrier zero).
If e.g. your partner transmits a slowly rising audio tone, and the center frequency of the spectrum is furthest down on 1 kHz, your partner has 2.4 kHz deviation at the AF level of the modulation. This will be a bit M-like shape of the spectrum, but you could also get a CW receiver listening with small bandwidth on the center frequency.
(Former packet addict, Co-Sysop of DB0HOM 1k2 AFSK and 9k6 FSK loserport here.)