what I am trying to understand is what happens to old conversations, they get pushed down in a linear sequential FIFO stack, or is there some sort of ranking system that shuffles visibility prioritizing it.
What @Chris described is the default Interesting sort order. There are actually two other sort options that you can choose from: Active and New.
Active will bump conversations with recent activity to the top, regardless of how old the conversation is. New is the sequential FIFO stack that you talked about.
Personally, I like using the Active sort option to keep up with all new post activity.