At first, I thought No; but then,
I started to wonder what is really happening, I mean, for as long as there is motion, there might be some currents being induced in the top as it spins but I have not put much thought into what the boundary conditions are, whether they are symmetric or not and what the currents might be...the relative motion of the steel is in one direction between the magnet and the center of the top and in the other direction after the center of the top
needless to say, these induced current should tend to stop the rotation of the top (no perpetual motion machine here) but that is beside the point, the point is that without rotation the attraction is what it is, with motion you now have the extra interaction between the two magnetic field, the magnet' s and the one from the induced currents, whether the effect of the induced current's magnetic field from both sides of the top simply cancel each other out and does not affect the attraction ...that, I wouldn't know at this time.
...just thinking aloud