The question is vague: what is meant by "wetting"? Is it a question of whether a drop of water will spontaneously spread over a glass surface, or whether a drop can be spread across a glass surface and not tend to reform into one or more drops or droplets?
First of all, the glass will have a surface covered by water vapor. The oxide surface grabs water from the air with a vengeance. A few hundred degrees C will get rid of most of it, possibly >300 C (sometimes for hours in a vacuum) is needed to get all of it. Of course there are different kinds of glasses; soda glass, which contains major amounts of the oxides of silicon, sodium, calcium and aluminum, is the most common.
A drop of water will not spread spontaneously on glass. The physics behind this is that water molecules like water molecules (remember "like dissolves like"?). The term "like" is not scientific: a better term is "cohesive energy," meaning the energy required to pull a water molecule out of the droplet. For example, oil and water don't mix - the attraction of water to water is greater than of water to oil, or oil to water.
This discussion can also be made in terms of surface energy, but I think is is more clear and more generally applicable to cast it in terms of cohesive energy, which is close in meaning to "heat of vaporization."
The glass surface obtains a hydrated coating by both physical and chemical adsorption. This means that the glass surface will look a little like water, i.e, the effective cohesive energy of the surface will be a little less like pure glass and slightly more like water. In the battle for water, the drop will still win but the hydrated glass gets in a few licks. The glass likes glass a lot and is not itself dissolved by the water.
Nonetheless drops of water can be spread over the glass by physical energy such as with a spatula (as in one of the referenced videos) without re-forming into drops or droplets. In this case the water is introduced onto fresh hydrated surfaces that it quickly hydrates all the more. Then the glass surface looks more like water to the water. It will take energy to reform the drops - they may not reform spontaneously.
So my answer is that glass can be totally wetted under some circumstances but not in the (unobtainable) purist of systems, and not spontaneously unless acted on by external energies.
Entropy of mixing, free energy of droplet formation and other complications mess up a pure discussion, but I think the above discussion gets most of it. The quantitative description of the concepts described above are used in industry from cosmetics to metallurgy and are founded in chemical thermodynamics.