If one was to build a web app, and an iOS/Android app that are designed to run as one (iOS/Android on the phone and web app on the PC), like how facebook works, can both apps interact with ethereum, to provide blockchain technology no matter what device a user is interacting with the app on?
Yes of course.There are two ways of doing it.
Installing ethereum in some machine, expose JSON RPC API, using web3js channels we can create both web apps and mobile apps. Because it creates the endpoints to interact with blockchain.
There are ethereum-light-clients, which can be added inside the mobile app itself, like running the node itself in the mobile. So the mobile app can directly interact with the blockchain network to which it is connected.