CloudReady is designed, first and foremost, to maintain the experience you get from a Chromebook in as many ways as possible.
This includes all of same privacy and security controls that you would have on a Chromebook (excepting features mentioned here).
Google provides a useful resource for reviewing what applications, extensions, and utilities have various permissions and access to your Google/Chrome Account:
If you visit that link, you may see that "CloudReady by Neverware" or "CloudReady free" is listed as an app that has full access to your user and permissions. You will also notice that "Google Chrome" is similarly listed (assuming that you use or have used Chrome on some other machine). This does not imply that CloudReady has permissions which it should not have to access your account.
In creating CloudReady for your use, we have rebuilt Google's Chromium OS, including their entire Chromium Browser, from scratch to include our careful improvements. In that sense, CloudReady is a replacement for Google Chrome, and so requires all the same permissions as Google Chrome in order to connect with your Google account, sync your settings, and do all the other seamless syncing that makes Google ecosystem so great.
Rest assured that we are committed to respecting your privacy to the same, if not greater, extent as Google. We never move your user information or data off of the machine which you install CloudReady on. We only access your user information and Google account using code pre-built into Chromium, which was written by Google engineers for the sake of syncing and running Google services.
If you have any questions or clarifications around this, feel free to comment below.