The Register New Volunteer Screen does not support only the field type "Time".
All type of custom fields from Contact object can be included in the "Register New Volunteer" screen except the "TIME" field.
The "Register New Volunteer" supports "Date & Time" field and only "Date" field but does not support only "Time" (Which show only Time) field.
The custom fields which are added in the Contact Fieldset is shown in "Add New Volunteer" screen. More information here for adding Contact Custom fields to "Add new Volunteer" screen.