Do MEMS accelerometers have a lower frequency limit?

There is no lower limit to the frequency response of the acceleration to output transfer function. As the other answers have said, they detect orientation, which means detecting gravity all the way down to DC.

However, be aware that all accelerometers, regardless of technology, suffer from the velocity to acceleration transfer function falling by 6dB per octave towards DC, and the position to acceleration transfer function falling by 12dB/octave, as the shaking frequency decreases. At lower frequencies, the same acceleration is going to correspond to larger amplitudes and higher velocities, so it will certainly seem like the sensitivity falls towards DC.

From what I recall, some accelerometers use 4_leg capacitive bridges, etched out of the top silicon layers to provide tiny suspended masses that respond to changes in force.

Because capacitance measurements have no lower limits (using AC_stimuli to detect bridge imbalance), you should be able to sense down to DC.

Such a lower limit would not make much sense and would render the device unusable for detecting the orientation.

A MEMS accelerometer will (typically) output the acceleration from Earth's gravity when it's resting. You will see this as "-1" or "+1" in the Z or Y axis, depending on its definition. This would not work if it could not detect frequencies all they way down to 0 Hz.