Is it possible (and in that case how?) to connect an iOS app, build with swift using xcode, to an Ethereum testnet? So for instance a user would be able to login and set or get a value which is saved on the Ethereum test blockchain?
yes, it is possible to connect with Ethereum with web3swift. This lib is not official from Ethereum but This lib can connect with Ethereum blockchain. For more reference hit this link https://medium.com/@shivangpandey195/getting-started-with-web3swift-1a2454481f70 and implement web3swift lib in your XCode project.