It depends of what do you want to achieve. APIs exposed for Sharepoint Online are not available on Sharepoint On-Premises, but you can access the existing APIs in Sharepoint On-Premises.
For example, if you want to work with lists, yes, you can use the library for that, but please understand our primary target is Office 365 (Sharepoint Online).
They key class to interact with a Sharepoint site is : https://github.com/OfficeDev/Office-365-SDK-for-Android/blob/master/sdk/office365-lists-sdk/src/com/microsoft/office365/lists/SharepointListsClient.java .You'll see is pretty straightfoward, and the only thing you need is an implementation of the Credentials interface to authenticate request using a mechanism that fit your needs. You can find several implementations here:
https://github.com/OfficeDev/Office-365-SDK-for-Android/tree/master/sdk/office365-base-sdk/src/com/microsoft/office365/http
I remember I used https://github.com/OfficeDev/Office-365-SDK-for-Android/blob/master/sdk/office365-base-sdk/src/com/microsoft/office365/http/BasicAuthenticationCredentials.java to authenticate against a test sharepoint installation without problems, but all that depends of you scenario. As long as you pass the correct implementation of the Credentials interface, it should work.
Regards,
Marcos
-disclaimer: I'm a dev in the Office 365 Android SDK.
