
You don't understand
A Google Profile and a Google account are not the same thing. I had a Google account for years before I set up a profile. You don't need a profile to use an Android phone.
If you have a private profile and it gets deleted, it won't affect your Google account. You will still be able to use all the Google services (except G+/Buzz/orkut) the same way you can currently if you don't have a profile.
If you decide to make your profile public, the only things that are required to be public are your name (my name's already on the web) and gender (typically easy to figure out if you already know someone's name.)
Anyway, delete your profile, set it up again, delete it again, rebuild it, let Google delete it...it doesn't matter. It won't affect your Android or any other (non-social) Google service you might use.