Yes.
I'm running iTunes
10.4.1 under El Capitan. It works beautifully. I briefly tried 11.4, and that worked to too. Turned out I didn't like the iOSification, single window, small artwork and the lack of cover flow, so I went back to 10.4.1.
Of course the store won't work under 10.4, and I presume 11, so you have to keep two copies of iTunes around, and two distinct music libraries, one for each version.
After deleting iTunes 12, by booting off a different disk before trashing, I rebooted, and installed 10.4 on my El Cap disk, used this script to rescue most of my library info (
Move Track info (playcount etc) from one iTunes Library to another.) and went with it. Named the App "myTunes", and the Library folder "myTunes". That done, and running, I made a a small secondary library "testlib12" for iTunes 12 to mess with, and reinstalled iTunes 12. This left iTunes 10.4.1 intact and functional, and when I option click on iTunes 12 I can choose my little 12 library, and have have access to iTunes store etc. There are some quirks, but I run 10.4.1 on El Capitan 99% of the time. There's another thread in Mac Apps and Mac App Store with some more detail.
This dialog can be dismissed, either manually, or by script, it's simply telling you that the store code in your lower version of iTunes is outdated. That's why you keep a copy of iTunes 12.whatever around too, so you can do modern store and sync stuff when needed. I just use the old iTunes for what it's better at than 12,
playing my music.