My advice to the OP would be to read/watch youtubes or whatever to learn his system and then do what he decides. One can see from the posts here that some of this two pump theory is way off base in my way of understanding things.
If me or you were manufacturing axles would we fill the inner cavity with grease? Heck no that would cost a bunch more money and cut profits.
So as others have posted it will take a boat load of grease the first time to fill the inner cavity between the bearings, since it came with mostly air in it.
Just think how many years or times it would take a double pump that just goes on the inner bearing to fill the cavity and eventually make it to the outer bearing. :h
In my opinion, the double pump folks that do not initially insure that the inner cavity between the two bearings are full, are running that outer bearing without a repack for as long as it will take for the inner cavity to be filled - two pumps at as time.
I have to admit that some of the posts here, I agree with, but how does someone who asks the question sort out the wheat from the chaff?