I have a Sony x800d with Android TV. Since you can't have 2 Google accounts on it I temporarily switched to a different Google account to access the US play store and download some apps. Now that I'm back to my main account will those apps receive automatic updates even though they were downloaded by a different account? After all they weren't sideloaded so automatic updates from the play store should work.
Different situation so this is technically speculation, but similar, I've tried similar with spoofing devices to make incompatible apps install but on the same account. In my experience doing that things that showed up in the store normally (such as people reporting to the dev that it worked so they marked it compatible) would update after the spoof reverted, but other things wouldn't. I've never tried the different account thing, but presumably it would work similarly where if it becomes available in the country of your main account it would start updating, barring things like purchased ones, but merely having it installed wouldn't mark it as compatible/available/whatever so it won't pull updates your main account can't on its own