No. What you are describing has absolutely nothing to do with Exchange or Microsoft, tt is simply the nature email.
You cannot design a system to handle email that requires administrator level privileges to install, maintain, and support and yet not have email readable by the admin. Sure, you can do all sorts of funky encryption/protection etc on the actual mail data once it hits the CEOs mailbox to make sure that it's unreadable by the admin. But since the admin is also responsible for mail routing there isn't anything preventing him from getting automatically CC'd on the CEO's emails, or capturing copies of those email messages in transit. Additionally, there's nothing that would prevent an admin at an outside company from intercepting email messages between his CEO and yours. Or for that matter, there's nothing preventing someone from sniffing the SMTP traffic from the ISP and getting copies of the email.
Email is not a secure method of communication. It was never designed to be, and anyone who believes that it is just has their head in the sand. The only chance that you have of securing email communications from prying eyes is to use encryption software to encrypt the message from the sender and decrypt it at the receiving end. Unfortunately, that makes the system too complicated for non-technical people to use, and if you lose the decryption keys then you end up with email messages that nobody can read, not even the intended recipient. Of course, there are systems that are designed to make email encryption much more user friendly and allow for key recovery, etc, but those all require some level of admin privileges (which means that you're back to your admin being able to read your mail).
And while we're at it, let's dispel the myth that you can lock down file shares so that your admin can't get at it. You can't. Your admin will need the ability to manage file permissions, and if they have that ability then they have the ability to give themselves access to the files in question. Your backup software will need access to the files to back them up, and that's another attack vector.
What all of this comes down to is very simple: technology requires technically competent people to manage it. Those people need administrative privileges to manage the systems, which includes the ability to get total access to everything on those systems. Therefore you have two options:
1. Hire trustworthy people while maintaining a system of checks to ensure that authority isn't abused.
2. Don't use technology.