Lightroom (or any other non-distructive editing program) does not edit your image.

It keeps your actions in a "separated area" (usually a sidecar file in XML format cached in memory) sometimes called "recipe" which keeps your last settings. For example I have a photo and I do the following edits in this order:

1. Brightness: +10
2. Contrast: +7
3. Sharpness: +3
4. Brightness: -2
5. Contrast: +5
6. Sharpness: -2

After each step LR will update the recipe and each recipe change will trigger the screen repainting of the same actual (raw) data and not a change of the photo itself.

Let's see how the algorithm works step by step, based on the edits above: (in the list below B means Brightness, C - Contrast, S - Sharpness).

   Recipe:          Algorithm:

1. C 0, B +10, S 0 -> RecipeChanged -> GetRaw -> ApplyRecipe -> ScreenPaint
2. C +7, B +10, S 0 -> RecipeChanged -> GetRaw -> ApplyRecipe -> ScreenPaint
3. C +7, B +10, S +3 -> RecipeChanged -> GetRaw -> ApplyRecipe -> ScreenPaint
4. C +7, B +8, S +3 -> RecipeChanged -> GetRaw -> ApplyRecipe -> ScreenPaint
5. C +12, B +8, S +3 -> RecipeChanged -> GetRaw -> ApplyRecipe -> ScreenPaint
6. C +12, B +8, S +1 -> RecipeChanged -> GetRaw -> ApplyRecipe -> ScreenPaint

That's why if you open the actual (raw) file with another program which doesn't have access / doesn't know how to interpret the recipe (even if there is an XML standard for that) the image will appear untouched.

When you "export" the file, in fact is applied the same pipeline as above IOW is taken the current recipe, applied to the original raw file and the resulting offscreen bitmap instead to be rendered (painted) on the screen it is saved in a file.

As you see, because these programs doesn't work with the actual photo (like e.g. Photoshop, PhotoPaint, GIMP etc.) the order in which modifications are applied is lost, the program editing engine being responsible of applying them in the what it thinks to be "correct" order.

So Tim Grey was right. Overall, it doesn't matter when you do your sharpening. Also, to clarify, "Zeroed" and "None" are just some recipes applied by default to all imported images from a batch to give you a starting point. You can freely change them. It doesn't lose anything.