Yes, that's doable. Example as follows covers registration and profile edit for both frontend and backend to assign a usergroup based off a field value.
Global
Triggers: onAfterUserRegistration, onAfterNewUser, onAfterUserUpdate, onAfterUpdateUser
Type : Usergroup
User: Automatic
Access: Everybody
Conditions
Field: YOUR_FIELD_HERE
Operator: Equal To
Value: YOUR_FIELD_VALUE_HERE
Action
Mode: Add Usergroups
Groups: YOUR_USERGROUP_HERE