Can I assign steps and send notifications to the form submitter?

Yes.

The form submitter does have a WordPress user account

If the submitter will have a WordPress user account then you can assign the step to the User (Created By) field. If you don’t see the ‘User (Created by)’ field in the ‘Assign to’ setting, go to form settings and activate the ‘Require user to be logged in’ setting in the ‘Restrictions’ section of the form settings.

The form submitter does not have a WordPress user account

You can assign the step to an email field.