There are two relevant cases:
1. The rotation is in a horizontal plane
In this case, the pole would be able to balance (at least to the extent that that unstable equilibrium is possible on Earth to begin with, and adding on any vibrations or other imperfections of the motion), and artificial gravity would indeed work within those confines. The direction of this artificial gravity would be at an angle to both the surface and its normal, which might make for some awkward geometry when constructing the station, but there's nothing wrong with the principle ─ the (constant!) direction of the acceleration in the rotating frame would just be identified as the local version of "down" in that frame, and that's that.
(Or, at least, that's the case in the limit where the length $\ell$ of interest (the height of the pole and/or human) is much smaller than the radius $R$ of the centrifuge. If it's not, as pointed out by Duncan, then there will be noticeable variations in the outward acceleration (outward component of gravity) at different radii, which will mean that the local direction of 'down' (i.e. the direction of $\vec g$ in the rotating frame) will change from your feet to your head. That'll be nauseating and distracting, most likely, but you'll still be able to balance a rigid pole ─ the only change will be that the angle of equilibrium will depend on the pole's length, and you'll need to hold the base to stop it from slipping.)
2. The rotation is in a vertical plane,
I.e. the axis of rotation is horizontal. In this case, the pole would not be able to balance, because the acceleration due to gravity in the rotating frame would constantly oscillate, including phases where it points partly to the side (so the pole would topple).
Artificial gravity in such a situation might partly work, in the sense that you'd be held down to the ground, but anything that wasn't firmly held down would jitter around, and it would be extremely nauseating.