Either private or public blockchains powered by Ethereum can be used with Ethmobile projects.
Even with Quorum private Blockchains.
Ethmobile projects run on top of mobile Go-Ethereum and provides an easy access to it's API.
Mobile native technologies such as Java for Android and Objective-C/Swift for iOS are the most adapted to write the best blockchain Dapps. And so are Ethmobile projects.