Essentially, if you only have two routers connected back-to-back via serial, and you don't have any other interfaces on either routers that are active, then you don't need to have any routing protocols for both routers to "talk" to each other via the serial connection, 'cuz they're directly connected.
And, yes, you're right about your scenario. PROVIDED you also include your Ethernet interfaces in the OSPF routing process, otherwise, their subnets will not be advertised, hence you won't be able to see them in the routing table (therefore, they'll be unreachable).
As for Loopback interfaces, they're also quite often used as "Router ID" to easily identify each router. Imagine trying to determine which router is which when you have dozens, or hundreds, of routers. Would you know each router's physical IP addresses? And by the way, if you use loopback interfaces as Router ID, you don't have to include it in the OSPF routing process. And if you have multiple Loopback interfaces, you can manually tell OSPF which one to use as Router ID with the "router-id" OSPF configuration command.0
If you need a good OSPF reference, try searching for "OSPF Design Guide" on Cisco.com. It was written by Sam Halabi (he also wrote a very good BGP book titled "Internet Routing Architecture") around 10 years ago, but is still very much relevant today, since OSPFv2 has not changed since its inception.
HTH
Cheers
