Does a stock email app auto-update? To clarify, two things:
1. I mean auto-updates to the app itself, not syncing to receive emails.
2. I'm not sure if there's a *difference, but I'm more interested in knowing about the stock apps/versions of stock apps that don't seem to have any way for you to manually update them yourself. For example, on my Galaxy S7 Edge (running Android 7.0), in the stock Email app, I can go into the Galaxy Apps store, or through the email app settings to the Galaxy Apps store to update the app; but on an Alcatel OneTouch Elevate I have (my previous phone)(running Android 5.1.1), there appears to be no way at all for me to update the stock Email app.

So, my question turns into: Do stock email apps, like the one on my Alcatel, auto-update? Does it perhaps get updated as part of the system update?

*by this, I kind of meant that I'm not really interested in knowing whether the stock email apps that you can manually update will also auto-update. So perhaps another form of the question is: If you can't update it, does it auto-update?
There is a global Auto Update option in Android 7.0 (possibly previous versions but I can't check now) which automatically updates all apps.

There is also a per-application setting. In case you have the global option off, then you can have that one enabled and it will still auto update. So be sure that both are off if you want the app not to auto-update.

By default, I believe the global option is on but that might depend on the phone.

For clarity, when an app is updated, we call that an update, when its data is updated, we call that a sync, such as downloading new emails as they arrive.

Stock apps are part of the system, so they will update when you accept a system update.