I'm certain this has been on everyone's minds for awhile, though I'm not sure if MGE can do this currently. It would call for per-mesh shading or some such thing, where a shader is applied to anything that has that enchantment mesh over it (or is it just a texture? No idea.)
I'm sure someone more knowledgeable than me will correct me but, AFAIK, all the MGE shaders are full screen shaders, i.e. the effect is across the full screen (I guess the effects can be minimised / hidden by the z-distance from the camera) rather than just a part of it, like a single model. Applying a shader to a single mesh isn't there at the moment. There also might be problems when a mesh crosses the boundary from what MGE renders and what the Morrowind engine does. Although I'm getting out of my depth here.
Indeed it can. The little known and less-used "hook texture" function allows any shader to be attached to a texture. There's only one problem here: the weapon effect is about 30 textures, flipping between them. Using 30 hooks will take up half of the 64 MGE allocates. If something could be changed (which might be a question for Hrnchamd in the code patch) to use a single texture, that could be hooked no problem.
Beyond that, I don't think we could make a shader that shades for specific effects, unless MGE has some way of knowing what enchantments are on a weapon (blue for shock, red for fire, etc).
I'd guess those are stored in lights. With a few minor tweaks to the shader hook code, and once I kick myself and work on the light code more, that might be accessible. Otherwise, just a shimmer could be done with MGE (as it stands now).