Jeremy of BAS uploading a short video asking the question, "Do you flush?"
Naturally, Jeremy explained natural senescence occurs in living soil and a flush is not needed.
One guy commented on his long term reusing of living soil, he performed a test and it showed he had higher sodium content. He attributed the higher sodium content to his automated watering.

How would the method of automated watering, be any different than hand watering for building up of sodium?

I can't think of any reason. The sodium buildup would have to be from his inputs.