Can an iPhone use OS X Server's Calendar service without enabling iCloud calendars? There are iOS devices in my household which do not have iCloud calendar syncing enabled. However, I would like to have a shared calendar that is contained within my household and not replicated on the cloud (iCloud, Google or other).

It seems that OS X Server's calendar service allows you to have a shared calendar within your household and presumably syncs when those devices are on your home LAN/WiFi network. All well and good.

The question is, would you be able to use the Calendar service from OS X Server without enabling iCloud calendar syncing?
Yes, you can add an OS X Server calendar as a separate account through Settings → Mail, Contacts, Calendars → Add Account → Other → Add OS X Server Account.

This is a completely separate account to your iCloud account. You can allow sync outside of your LAN by forwarding the relevant ports.