@Linux
I have a LineageOS phone without Google Play Services. My Facebook account is deactivated. But recently, on my phone, I did get the WhatsApp app via an anonymous connection on the Aurora Store, due to my former workplace requiring this (and also some friends use it).
It does seem to be running in the background, given that there are notifications from it. The app itself is unopened. So, I've just changed it to not allow notifications.
I'll try turning my phone off again and then back on to see if the app will be running upon reboot.
Okay, I turned it off, and left it off for about 15 minutes. Upon rebooting, the phone indicated that three apps were running (but not WhatsApp), and it said that WhatsApp was last running 17 minutes ago. So, it it currently does not seem to be running on its own.