Get list of all groups from AD user source?

Can I get a list of all AD groups from an AD user source?

Short answer: sure.
Long answer... From my experience, this can get big quick because each user can have a unique list of groups. Some of the AD users in my user list have like 50 groups they are in.
There is likely a way to slim down what groups you want to view though - you can Softerra to query your domain LDAP servers and find an effective way to do this.
If you want, I have an LDAP script that I stole formatted to be able to query an LDAP server and return results.