Will a capsule of pau d'arco save my arbortivitae from root rot??

No. First of all the roots are very wide spreading, one capsule at the trunk will do nothing. I'm not even sure pau d'arco would work on the root rot pathogen. Baking soil up against the trunk is bad, trunk wood does not want soil banked against it. Also changing the grade under the arborvitae will either smother the roots or expose them to cold weather.

We don't know what pathogen is causing the root rot, there are many. If fusarium, the pathogen is in the soil and wet cold soil may allow it to grow. If the ground is moist, is there some way to dry it out? Only thing I remember having even a slight chance is sulfur sprinkled over the area and worked into the soil..........oh high pH soils. I wouldn't do this if your soils are already acidic.

I have a standing water issue -- it is really in the neighbor's yard but it is affecting my beautiful 12 foot high arborvitae hedge! 3 of my arborvitae died and it seems like they just plain rotted. If I open a pau d'arco pill and put it at the base of each bush will it help protect the bush from root rot? Can I bank up soil around the bush to protect it from water or will that just smother each bush? What about working calcium into the soil to halt rot? Any other ideas?

Fluffernut is correct.

I would only add that they only solution to your problem is to address the drainage issue. Either through digging a dry well (feasibility depends on your subsoil, and the depth you would have to dig to get through the impervious layer in the subsoil), or digging a french drain (again, depends on the lay of your land, and which direction it slopes, and if you can direct the french drain to an appropriate end, like a street or storm drain, rather than another's property.