I would say it's beneficial for replacement gears as they have an undetermined shelf life and it can help prevent corrosion.

i do not think a phosphate coating will be useful. the problem with hypoid gears is that when loaded it is very difficult to get a sufficient lubricating film between the mating parts. depending on the point of contact there is either excessive sliding (where the adhesion of the lubricant will be insufficient to establish a stable lubricating film) or there is excessive pressure (where the lubricant is simply pushed away). under both conditions you will have metal to metal contact which will result in local welding. therefore lubricants for hypoids contain so called EP-agents - a additive based on S and P that gets included as a pollutant in the weld - making is a lot less strong so it can be sheared easily, leaving a smooth surface. the operating conditions in a hypoid drive are such that a phosphate coating will wear away quite fast and thus is not of much use.

testing can be done on a loaded gearset. tests that are used are twofold: the one under high torque low speed, the other one under high speed and lower torque. the first test will give information under high pressure conditions, the second on what happens under excessive sliding (which occurs at the top and bottom end of the gear).