You cell phone carrier mining data from your phone is the least of your worries here. They don't care about your Bitcoins. I'd be more concerned about data-stealing malware, which continues to appear in ever-nastier forms for Android devices, or physical loss of the phone. I trust my phone for a lot of things, but not to store important passwords.
If you decide you want to try it, it's important to take steps first to secure your phone. If you haven't already done that, there's a decent Gizmodo article here that will help:
http://gizmodo.com/5995254/five-simple-ways-to-keep-your-android-malware+free.
