The simple answer is yes, and this article explains how.
Otherwise, go through this to turn on automatic downloads:
OpenSettings.
Turn the slider on/green besideAutomatic Downloads.
Repeat these steps on every rig you want apps automatically added to.
Tap theApp Storeapp select your photo in the top-right corner.
TapPurchased>Not on this iPhonetosee all apps you’ve bought that aren’t installed here.
If you’re using Family Sharing, tapApps>My Appsto view your purchased apps.
The purchase grants your Apple Account the right to use that app.
If it is, everything will work as expected.
Most apps are available in Family Sharing, but not all are.
Those you do have to buy again.
