Is it possible to align a mems gyro to approximately true north with no external data input?
MEMS gyros are not (yet) accurate (and stable) enough to do that, but laser-based gyros (FOGs and RLGs) are capable of directly measuring the 0.004166&deg;/sec rotation of the Earth and determining the axis of that spin, thereby aligning themselves to true North.

If you'd like to learn more, search on the phrase "Strapdown Gyrocompass Alignment".