Absolutely, arch will teach you quite a bit. Not nearly as much as Gentoo though. If you're going for learning how things work at a core level Gentoo is a fantastic place, though of course LFS will be better though more involved. I'm glad you're willing to take the harder path though!

As for arch, it'll teach you about mounting, user management, partitioning and partition management, an overview of how to set up a system and a few of the options available, and make you more comfortable with the command-line. With a few exceptions, that's about it. you can understand what makes arch arch in less than a day.

As for Gentoo, it's a guided experience that will teach you all of that but much, much more than arch will. With arch you could look more into it, and arch will be very well documented on what to do, but Gentoo will lay out the choices clearer with an explanation as to why. What is SystemD and why would you use something else (or, why you need so much to replace one thing?) How is networking built up? how do package managers work? What different kernels are available and why would you use them? What file system should you use? How does networking work on Linux? How do you install a tarball? What are firmware and microcode?

Just look at the index (legend?) on this page Gentoo Wiki and then this page Arch Wiki (on the left.) You'll see how much more Gentoo goes over

To be clear, I use arch on my main system, it's a fantastic OS and I'll likely use it until the heat death of the universe, but installing Gentoo, following the links, and searching up what I don't understand has taught me much more. LFS will, of course, teach you essentially everything though. It's a great option, and you're in for a fantastic journey. Once you're done you'll be the most impressive person in the room, if that room is full of us linux nerds

When I was in your position one of the first things I did was to install arch. It is very similar to gentoo but you don't have to compile everything yourself which is just more practical in the beginning. You still have to learn all the basics and the arch wiki is one of the best of it's kind. I am myself to install gentoo as a next step but the procedures are very similar to arch. Also with arch you can reinstall the system in minutes (with enough proficiency) but on gentoo or LFS this depends on how beefy your computer is. With a regular desktop you will sit there staring at 5the compilation for quite some time which was the biggest drawback for me. It will cost you more time to repeat a process and for me the best thing on arch was to srcap everything and restart to try something new.

One last thing: You will always learn as much as you are willing to understand. You can install gentoo and arch withoit any problems by just following the great wiki pages but you won't learn much besides typing some commands. But doing some research wbile installing will help you far more. Also learning linux is a process. It's not only about the system itself but rather about the community it's culture as well as the philosophy behind it.