What is sensor drift?
I assume you set the first momentum of your true measure to $\mu=0$, so your  question actually reads


  gyroscope with sensor drift does that mean that $E[f(x)] \ne \mu$?


No. It might still be the case that the sensor value, in the long term, drifts centred around the true value.

The thing is that $f(x)$ is a random variable with non-zero variance and a time dependency. That means: If there's drift, that random variable is not a stationary process.