From what little I've read, fat separates from the water when frozen, and then gets back together again when thawed, but isn't quite the same aferwards. As far as how well avocado freezes when thawed, I haven't a clue about that.
A side note about avocados in general that I just found out. I sliced an avocado in half, used one half. I was too lazy to do what I always do, squirt some lemon juice on top and wrap it in plastic and put it in the fridge, to hopefully make it last. One night I was just too lazy and put the avocado half in the fridge without lemon juice on top or wrapped in plastic.
To my surprise, the bare avocado half, left on its own, in the fridge, not wrapped, had a top skim coat of dryness that I scooped off and discarded. The half of avocado underneath was fresh still, no dark areas. From now on, I'm going to split them and place the seeded half inside the fridge as it is. I'll just skim off the thin top layer that develops.