With this indicator removed you can still use MATE Tweak to save layouts and switch to layouts you have saved. I have been using my main home computer with this indicator removed for months now, which I actually had forgotten about until this post came up and I have changed my layout and saved it. I just tried it again now and it worked.
What does happen, though, is that many (nearly all?) of the predefined layouts (like Mutiny and Cupertino) no longer show up in the MATE Tweak list for you to choose from. (I only see my own saved layouts and “GNOME2”, but I’ve also removed other things like Plank that are needed by some layouts.)
@Rarmorog I don’t know how to remove this indicator and keep the layouts showing up, but you can always reinstall it if you want to change layouts and then uninstall it again.
If you really wanted to try, it looks like the “meat” of the indicator package is are the binary itself
/usr/lib/x86_64-linux-gnu/indicator-session/indicator-session-service
and the systemd service
/usr/lib/systemd/user/indicator-session.service
You could try keeping the package installed but delete the binary or edit the systemd service file so it doesn’t start. You may get errors since the package would be essentially (intentionally) broken. [Edited after reading closer the post that @mdooley linked to.]