Yes it can be converted but you need to be using Google Apps for business.
https://support.google.com/a/answer/60217?hl=en
My client was the same. Tried to convince him to move to Office 365 and use Active Sync but his website and employee emails were already with Google.
He insisted on being able to sync his
Google Gmail account with his
Microsoft Outlook on his
Microsoft Windows office computer and his
Apple iMac home computer, along with his
Apple iPhone and
Apple iPad.
I was trying to find a way to get Linux, a PS4 and a Sun Workstation added to the mix but ran out of patience.