It is possible to have mod and working update, I had it before.
The Apple login isn't like the Google login. A person's Google account in-game goes through the play store, and since we're going around it, Google accounts can't be used. Unless someone has their device rooted and patched, so unsigned apks can be plonked on top of signed ones. That would let someone with the play store version log in, then "update" the game with the unsigned apk, and still be logged in with the mod.
Apple login is just signing in and retrieving the save data attached to the account, like FB on other mods. It doesn't have anything else to do with the app. For this game specifically, I used to be able to log into the modded version, but now can't. Something must have been messed up in the process of the mod getting updated, because it was possible before. :/