I want to create an animation with the following effect. Imagine a wireframe rendering of an object being “filled in” starting at a ground plane and moving upward until the entire object is now filled in with it’s material. Sort of like if the object was a completely transparent vessel and you poured in an opaque liquid. I’ve been scratching my head over this one for a while. Anyone care to take a stab at it? 
Well the computer’s rendering now so I can’t make an animation to test, but I think this will work :
Use two meshes, one a wireframe material, the second the same material but not wireframe. To this material give an empty-orientated blend texture multiplying alpha (adjust colourband). Set the empty beneath the object and set a location keyframe, animate it moving upwards. Sorry I don’t have time to post a clearer explanation.
This community is amazing! I ask a question that I (foolishly) think is going to stump you all and I get an answer that works within minutes! 
I am in awe!! :o
I just tried it out(the method Rysy 2 posted), it works to apply a skin to the object(covers up the wireframe with material), but it does provide a subdivided surface.
ie. Rather then looking like a glass filled with wine, it looks like a glass coated with wine.
Not sure what you are looking for.
Another approach may be to use a lattice to distort the solid filling the vessel. I’ll try it out, sounds like an interesting challenge.
Glad to help ! I feared my explanation wasn’t clear enough, I was a slight rush.
To make it look more like liquid filling an object, just scale down the non-wireframe mesh very slightly.
You can also try the Build effect.
And for the liquid filling, well, that’s more difficult because you must also fake the top surface of the liquid as it goes up as the liquid fills the container. But I don’t think the original question involved liquids.
Stefano