Since Google is blocked in China, the default process for installing Android applications there is also to download an .apk from the internet and install it manually.
It works without a hiccup on my phone running LineageOS. I haven't tried on something running stock Android.
But it leads me to suspect that there isn't much standing in the way of distributing your Android apps this way outside of China, either.
Sanctioned Russian banks distribute their apps as self-updating apks. It's much, MUCH worse with iOS — Tinkoff tried publishing an innocuous-looking app that turns into their usual bank app after you open a "secret" deeplink for example.
Two things are problematic, though: 1) app stores got normalized as a way to distribute apps to the point of people being afraid to sideload, and 2) the fact that you can't distribute an iOS app without Apple's permission is utterly bonkers.
It works without a hiccup on my phone running LineageOS. I haven't tried on something running stock Android.
But it leads me to suspect that there isn't much standing in the way of distributing your Android apps this way outside of China, either.