What is the general range of the structure oscillation frequency in MEMS gyroscopes and/or accelerometers?
MEMS accelerometers have a relatively high resonant frequency- tens of kHz. For example, here is the datasheet for the classic (aka obsolete) ADXL150, which has a resonant frequency of 24kHz typically. 



The precision navigation-grade ones (non-MEMS) have a relatively low resonant frequency- more like 1kHz. 

Sensitivity is directly related to resonant frequency (the square root of the ratio of spring constant to mass is the angular frequency) so you can expect some consistency in the resonant frequencies of the structures of different designs. They normally have some kind of end stops to prevent damage in case the fundamental frequency gets excited with power off or whatever. 

I believe they're almost all force rebalancing types these days, so the mechanical resonance should be greatly damped when they are in normal operation.