I don't think it makes a difference. If the external torque stays in the same direction, it will raise the gyro/top that is at 90 degrees or even if it's below the horizontal.
I am assuming that rolling resistance is the cause of the rise.
In a normal top the rolling resistance is a torque about an axis which is always horizontal, (or, to say better, an axis which is always parallel to the spinning surface), whatever the angle of tilting of the top.
The base with the three ball bearings makes the picture more complicated but I believe that there is still resistance to rolling with the same effects of the rolling resistance of a normal spinning top, and that this resistance is still a torque about an axis which is always horizontal.
If the gyroscope is tilted by 90 degrees, the axis of the rolling resistance torque becomes aligned with the axis of the gyroscope;
in this condition the component of the torque wanting to tilt the flywheel disappears, and the only effect of the rolling resistance is that to slow down the spin speed of the gyro.
When the gyro is below the horizontal, the effect of the rolling resistance becomes reversed, it pushes the top downwards instead of making it rise, so the gyro can only sink down at this point, since the other torque too, (the friction torque about the vertical axis), is in the direction to make the gyro to sink down.
I desume from my experiments that generally friction torques about the horizontal axis, (like rolling resistance), make the top or gyro to rise, and that friction torques about the vertical axis instead, (like rotational sliding friction), make the top or gyro to sink down. Anyway when I tried to measure and calculate the magnitude of the forces in play, it seemed like rolling resistance by itself is a bit weak for to justify the speed of the rise, so there is something I am missing.
For this reason I was curious about the behaviour of this new gyroscope.
Maybe Jeremy could tell us if the gyroscope can rise from a very tilted position.