Will apk installed manually (not from play store) receive notification when update becomes available?

you will receive updates / see the app in the Google Play "installed apps" tab only if the two conditions will take place:

• the APK package name is the same as the one uploaded to Google Play
• the keystore used to sign the app in the play store is the same keystore used to release the apk you install manually.

Late Update 09/30/2019

These days - As long as the package don't part of the user's apps library in google play - the app won't receive automatic updates from the play store.

App will be part of user's play store library only after it installed previously in the past by the same user, or after the user explicitly went to the app's page in the play store - and pressed "update" for the first time after it installed outside the play store.

The two original condition I mentioned in the original answer - are still correct.

To preinstall your APK, you need to be the device OEM; how it gets done depends on your exact environment. If your apk has no native libraries internally, you can safely just place the apk in the firmware image (in the same location with the standard apk suite). Beyond that, you could (for example, similar to what I've seen in some Motorola devices) create a special directory (such as /preinstall) and have a script perform "pm install ..." for each file in that location for those items not already installed.

Regarding updates, as people have commented: no problem since you're not changing the package name. Just be certain to increase the package version for the store upload. Also, for safety, upload the package (older version, non-functional is ok) to the store in order to reserve that package name on the store -- otherwise someone could place their own on the store before you.