It seems that single-port devices like quartz crystals, ceramic resonators (including ultrasonic devices), BAW & SAW resonators all have an equivalent circuit of the same type:
simulate this circuit – Schematic created using CircuitLab
Co dominates at low frequency. Cm resonates with Lm at the series-resonant frequency, where Rm dominates. In your BAW graph, series-resonant frequency is approx. 6.263 MHz.
Above series-resonant frequency, reactance is inductive for a small span. In your BAW graph, this inductive region spans from 6.263 - 6.272 MHz.
At a frequency slightly higher than series-resonance, Cm combines with Co to yield anti-resonance (sometimes called parallel resonance). In your BAW graph, this is around 6.272 MHz.
Above the anti-resonant frequency, reactance becomes capacitive, and Co dominates. So yes (to answer your question), a SAW likely has a similar progression as your BAW example.
Quartz crystals have numerous spurious resonances which are often not characterized - only one dominant resonance (shown by the equivalent circuit above) is spec'd. Harmonic resonances are often not spec'd either. Some high frequency crystals are made to select 3rd, 5th, or even 7th harmonic - only the most active is spec'd.
I'd expect that any piezo devices have similar spurious resonances. It is sometimes possible that spurs can dominate in some circuits, but this is quite uncommon.