Yes, I guess this is what self-taught looks like. Although I have seen the use of mnemonics to remember the order of things in many contexts in music, including formal teaching. I thought some of these were universal: FACE and Every Good Boy Deserves Fudge for the note names on the staff, Father Charles Goes Down And Ends Battle, Battle Ends And Down Goes Charles' Father.

By this time I must admit that the random note playing is just an activity that I enjoy improving at independently, while I do think it's also making it easier for me to pick up new pieces quickly.