What does it look like when chat and form are enabled?

I understand that If we enable multiple features, they would be presented in this order:

1. Self service
2. Live chat (only displays if outside office hours AND no agent available)
3. Phone calls
4. Contact forms (only displays if outside office hours OR no agent available)

Since an end user may not have time for a chat or prefer to work asynchronously, we would like to provide self-service first, then the option to choose between chat or the ticket form. On the Zendesk site's widget, the behavior seems to be self-service then chat only (with the pre-chat form enabled, rather than an actual ticket form).

Is there a way for widget (classic or messaging) users to have an option between chat OR ticket form, or do they need to go through chat before the fallback form?