No.
As the rotational energy dissapates, the gyro will precess and then fall.
bert,
Then keep it spinning with an onboard motor.
There are plenty of examples on YouTube, or you can reproduce the behavior on your own.
Don’t play dumb. You have used the word “precess” correctly, in context. You are obviously intelligent.
However, a gyroscope in a three axis gimbal will NOT “fall.” It will simply spin to a stop when its rotational energy dissipates.