(Assuming your post isn't sarcasm)Sure it will.
That's one of the reasons Inertial Navigation Systems "drift".
Ever heard of a Foucault Pendulum?
A inertial guidance system drifts only because its frame of reference changes.
A gyroscope does not precess unless the frame of reference within which it operates moves.
Forget the Foucault Pendulum.
Buy a gyroscope and do the experiment for yourself.
Mount the gyroscope in any orientation on its tripod support. It will still have two, mutually perpendicular axes of free rotation.
Spin up the gyroscope on a stationary table. Observe it for fifteen minutes. It will not precess.