Using Kerberos Authentication on F5 without APM

Yes it is required.

That said, if you make the external virtual server FQDN the same as the service principal name (SPN) of the server behind the VIP, you can pass a Kerberos ticket through the VIP without APM. The client is making a ticket request, and its ticket is based on the SPN that it knows, which it derives from the web URL. APM can actually proxy Kerberos traffic, so the client can submit a Kerberos ticket directly to the VIP, and APM can request a separate ticket (different SPN) to the backend server(s).