Does a magnetic field do work on an intrinsic magnetic dipole?

Yes, of course that if a field - magnetic field - is able to make a bar magnet rotate or move, it is doing work. The statement that magnetic fields don't do any work only applies to point-like pure electric charges.

Magnetic moments may be visualized as objects with a forced motion of charges (solenoids have the same magnetic field as bar magnets), and if something is moving, the magnetic force is becoming a force that does work.

In terms of formulae, the magnetic force on a charge is $q\vec v\times \vec B$ which is identically perpendicular to $\vec v$ and that's why it does no work. However, forces on magnetic dipoles and more general objects don't have the form $\vec v\times$ - they're not perpendicular to $\vec v$, so they do work in general.

I'm going to take a risk and try to answer this, even though my answer is different to Lubos's and he does have a reputation that is overwhelming right compared to mine.

Static magnetic fields don't do work, so the work comes from the magnetic dipole itself whose internal energy is affected by the external force that positioned it in the static magnetic field in the first place.

It is the electric field that does the work, not the magnetic field! When one has current in the loop, it can undergo a voltage drop or rise according to the inductance of the coil. Inductance relates to the electric field and its work.

See: http://en.wikipedia.org/wiki/Faraday%27s_law_of_induction

"The induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the magnetic flux enclosed by the circuit.[14][15]"

If the dipole is still, of course there is no work on it! When it moves, there is a change in the magnetic flux within the loop over the time of its motion resulting in an impulse (electromagnetic force times the time). This is classical physics. The electrical impulse changes the momentum of the current inside the loop, either gaining or losing energy according to the work done or received. If there is zero current, there is zero dipole!

Further even with an electron there is precession in a magnetic field, which results in additional motion of the charge elements of the electron in time. As the field goes from weaker to stronger, the precession of the electron increases precisely to accommodate the work done on it! See: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/larmor.html for detail!