When I look at my list of mods on Nexus Mod Manager, the update.esm is not checked. Shoudl it be?

It doesn't matter, It gets forcifully (Did I spell that right? lolol) loaded on startup whether it's ticked or not.

I believe that is a mechanism that Bethesda uses to patch the game. It may be a hold over from the day one patch or it maybe how it works now for incremental updates like the beta patch is doing. What you could try is if you are not using the beta, check the size of the update esm, join the beta, see what the change is in size. Sorry, I did not think to check this before I went with the beta, and I am not changing it back now.