Is it possible to backup and restore an app with data via ADB? Basically, I want to install an app with my settings already configured to a bunch of phones.

My thinking was


Install app on phone 1
Configure
Dump app and Data to PC
ADB app and data to phone 2
Repeat step 4


I would rather not root, but it's a possibility.
The answer is: It depends. It's the way supposed to work:

adb backup -f myapp.ab -apk com.myapp # backup on one device
adb restore myapp.ab                  # restore to the same or any other device


But an app can "opt out of Backup" declaring ALLOW_BACKUP:FALSE (see: adb backup not working for certain app), in which case (without root powers) all you get is a 41 byte (or in some cases 0 byte) file with the backup header but no contents.