Ukulele, like singing, doesn’t require any knowledge of music theory or the ability to read music.
I’m a music teacher, and this doesn’t mean that I support illiteracy in music—but to deny it would be actually living in denial myself. So I try to combat the state of affairs.
You would be surprised, however, how much music theory impacts you because you have heard music all of your life, and the lion’s share of the music we listen to—regardless of style—tends to follow the rules of music theory (and the stuff that doesn’t is so avant garde on the classical end of the spectrum that most people haven’t heard it).
That’s why a G7 to C sounds “right”...you’ve heard what we “music theory” people call an “authentic cadence” in most of the music that you’ve heard throughout your life.
Just know this...if you start learning ukulele, and liking it—there is a whole world of music theory that you can start learning more about which will help you understand why things work—and sometimes, to know why something doesn’t work. There are plenty of errors in the Yellow Book, and I find them with my ears before I analyze why they are wrong with my brain (and what should be done about the error).
So...for now, learn chords, play, sing, and have fun. And if you’re ready for the challenge some day, start learning about theory.