if you can't find information elsewhere then i doubt theres a clear cut answer for users outside US. but lets see what works. my app is official, maybe because i'm an 'earlier' adopter (went to play store or maybe amazon store to dl, VERY long ago), also my amazon account started off as a pure US account (but now my CC/shipping address is all SG).
i'm guessing the reason why you want to allow automatic updates is to get the new features? my app is still on 4.2.0.34, while the one in play store now is 4.6. looking at the screenshots from play store, there are quite a bit of differences. i'll update it in abit and let you know if it breaks.
[updated]
i won't say what i do is going to work for everyone, because it is obvious users here have different experiences with anything amazon... sadly, no one knows why.
so, i updated app in phone using amazon appstore, accepted new permissions, previous on-device books stayed on-device, download a few archived from those in cloud and things work as usual. read a page in a book and added mark/note, PW got synced immediately to the next page and the note appeared too. i also added a new highlight/note from within the PW.
next i went on to uninstall kindle amazon from a tablet, and reinstalled it using google play from chrome. re-dl the book being tested, at opening was prompted to go to the furthest read location and both notes showed up.
unless in the coming days my apps breaks, i'll say you are good. in fact, you probably don't need to go through the hassle of installing apk, and i've proved it in the last 5mins.
https://play.google.com/store/apps/details?id=com.amazon.kindle&hl=en
http://www.amazon.com/gp/mas/get/android
just click on the links from your android device. let me know if there's geo-lock in any of the steps.