I note that on registration, other fields are pulled from the individual's profile, but the State shows a pull-down, so that the user must select the State.
Is it possible for it to be populated from the profile also?
The state field in registration DOES pull from the user profile. Of course, the value in the profile must match exactly to the values in the dropdown of DT Register. You can edit the dropdown field in DT Register to match existing values in your profile... or you can build a profile state field to match.