Spring for android is useful if you need:
A Rest Client for Android
Auth support for accessing secure APIs
Given your question you say that you will use a RESTful Service. So my answer is that it can be useful to you.
Spring Android will not provide Depencency Injection support, Transaction Support, etc, etc.
I use an android opensource framework that integrates with spring android and simplify your coding: Android Annotations. This will reduce your code and give you a sort of Depencency Injection.
An other option to get Dependecy Injection support is roboguice.
Here you are a tutorial that explain you how to create a RESTful android application with spring: http://blogs.burnsidedigital.com/2012/08/how-to-create-restful-http-for-android-in-4-easy-steps-using-spring/