The only involvement with music I had growing up was choral, where you can successfully avoid learning any actual music concepts, because a good ear will do. I finally took up the guitar about 8 months ago, and apart from the instrument itself, I actually had to learn music[1].
Fast forward 8 months of steady practice, and while I'm certainly not going to be putting on a concert anytime soon, I've gained a lot of skill, which is making it a lot more fun. I'm playing music in more than just first position, improvising my own melodies and chord progressions in a few different keys, accidentally discovering parts of songs and sometimes learning the rest, etc. All without a teacher.
So...
1) You don't necessarily need to push a child to practice a musical instrument in order for them to find enjoyment in it later in life.
2) You don't necessarily need to arrange for formal lessons in order to find enjoyment in an instrument later in life.
Though I will say I benefited from access to DD's guitar teacher, who was able to point me in the right direction for where/how to get started.
[1] Well, technically, you can achieve a certain competency in guitar without learning very much at all about music, because tabs and power chords. I chose not to. Besides, I originally got into it to help DD.
