So in theory by knowing that leveling is tied to number of encounters overcome (if not a specific number), I could modify my play to engage with more encounters per session in order to speed up character advancement.
Well, yes and no because it depends on how you define encounter. If you talk to the butcher, the baker and the candle stick maker that doesn't not mean you just had 3 significant encounters. If I track it at the encounter level, I just jot down some summary notes after the end of the game. I may have some set pieces/encounters in mind when the game starts but that's no guarantee of what direction the players will take the game.
Much like the pirate's code, it's more of a guideline really. Being that fuzzy about how things work won't work for everyone of course, but for campaigns that don't have real story arcs it was the simplest solution I could come up with that rewards all pillars of D&D.