No, what you get (assuming a constant diameter of the tube without dents or shape changes) is that the magnet will induce a stronger magnetic field in the wall that is closer which will push the magnet towards the middle.

It will overshoot a bit (but not as much as the original deviation) and so on until it goes smoothly down the center of the tube surrounding it without touching the walls.

Likely there will always be a slight wobble but eventually that should become too small to detect.