possible?
Yes. You may want to check some settings, though. Google Play may not update on "metered" connections, so you may need to be connected to wifi.
Also, if the apps were installed by another app, then you need to update via Google Play once manually so Google Play is the "installer of record". After that, Google Play should be allowed to do auto updates. It may not be able to auto update really old apps that target an older api. I forget the details about that.
JustBeginnez Google Play Store App Info -> App Battery Usage -> Unrestricted
Might be worth a shot, but in one of my profiles Google Play updates things in the background when the battery usage is set to optimized.