A ferromagnetic material, such as neodymium, has nonlinear magnetic properties. But before discussing what would happen when making an electromagnet out of an already fixed magnet, let me back up a bit.
Suppose you take a iron nail and wrap the wire around it and attach it to a battery. The iron nail's ferromagnetic material, acting as the magnetic core, greatly increases the electromagnet's magnetic field strength. But only to a point.
When low currents are run through the wire, the electromagnet's magnetic field strength will be approximately proportional to the amount of current. If you increase the current, you will proportionally increase the magnetic field strength. But eventually, if you increase the current past some point, the magnetic field strength will not follow. The core has become saturated in this case. when the core is saturated, increasing the current doesn't have much of an effect on the magnet's strength.
After driving the core to saturation, suppose you remove the battery. You will find that the iron nail still has a little touch of magnetism left on it. Bring it close to a compass and mark which end of the nail is North and which is South.
Now repeat bringing the electromagnet into saturation, but this time reverse the polarity of the battery. Remove the battery and bring the compass back. You'll see that the iron nail's residual magnetism has reversed polarity.
This process where the core's residual magnetic properties "remembers" what the magnetic field strength was in the past is called magnetic hysteresis (there are some other words to describe the phenomenon too).
The residual magnetism caused by this sort of "memory" isn't very strong, and its not the best way to make a standing magnet. Your neodymium were probably made by melting the neodymium and letting it slowly cool in a high intensity magnetic field. But my point is that using a ferromagnetic material in an electromagnet can change the material's magnetic properties even after the external current has stopped.
===========
Okay, so here's the point of all of that. If you were to take an existing fixed, neodymium magnet and make an electromagnet out of it, here is what would probably happen.
(I) The direction of the wire winding and the polarity of the battery are such that the magnetic flux density reinforces the magnetic field intensity (i.e. the electromagnet characteristic N/S are in the same direction as the standing magnet):
...I'm guessing not much will happen. The standing magnet is already in the point of saturation (as it was designed to be), and making an eltromagnet won't help its magnetic field strength significantly bigger.
(2) The direction of the wire winding and the polarity of the battery are such that the magnetic flux density opposes the magnetic field intensity (i.e. the electromagnet characteristic N/S are in the opposite direction as the standing magnet):
...In this case the magnet's strength will be reduced, at least temporarily. I'm not sure if it would permanently weaken the magnet, but if brought into saturation it might, at least a little. On the other hand, with experimentation, you might be able to use this setup to temporarily turn a standing magnet "off" for awhile. Turn the current on and a magnet acts like a normal piece of metal. Remove the current and it goes back to being a standing magnet again. But again, I'm not positive what effect this would have on the long term life of such a magnet.