Yes, it can!
In Step 2 (BUILD SIGN UP FORM) of the Form Creation Wizard, look for the Actions tab in the sidebar:
Type in the Tag(s) you want to add to contacts submitting this form into the field below Add Contact Tag(s) to Subscriber.
Please note: this function is available only to Automizy Forms. If you use your existing forms via Autodetect feature, you should create an automation that adds the tag to your form subscribers: