The random component I assume to be gaussian (thermal noise, for example) and therefore symmetrical around the real value. It's obvious we can remove this type of noise through averaging (of which the core operation is integration).
The non-random component I assume to be a skew that can be calibrated out.
With these two assumptions in mind you can see that yes, it's indeed a random walk, but a very well behaved one.
As far as calibrating out the skew, of course you can do that to some extent, but it's not a magic bullet. The Minuteman periodically measures skew and even applies equations for the change in skew with acceleration. The problem is that skew is not constant; it changes with time, changes with temperature, changes with position, and changes randomly, so you can't just calibrate it out. That's one reason why missiles use strategic-grade IMUs for a million dollars rather than a commercial-grade gyro for $10: you're getting drift of .0001º/hour instead of .1º/second.
Short-term random effects (as in, the part of the gyro's random walk error significantly higher in frequency than the inverse of the integration period) will get cancelled out by integration, assuming they're Gaussian.
Long-term random effects (mainly from time and temperature like you mentioned) will instead tend accumulate with integration aka worsening with time.
P.S. great fan of your many ventures into retro tech, keep them coming!
