Would boxing complement Shotokan karate?

Moonlighting in another style would be very good for you. It seems like your school is very traditional and almost reminds me of an Aikido school in the way of, "less sparring, more technique". Personally I think that's a bad way to train because it makes you get the wrong feel about fighting. If you're doing it for a hobby then its no big deal, but if you want to compete than its a good idea to look up something else. I've studied Shotokan Karate a bit, just to learn about it, and I've found its a decent style. It still has the "old school" mentality you find in some styles but its overall not bad. Though if you're going through lax training, maybe you should look for another school that has a similar style that you can get more sparring and competitive training in. After all, you can practice a technique 100 times, but if you're not used to doing it against someone who's trying to hurt you in the process, you're not gonna be ready when the time comes to use it. Try looking for something like Taekwondo, Tang Soo Do, Kickboxing, or even just a different Karate school. This way your training wont go to waste and you'll be able to transition well.