After extensive time and testing I can say with certainty that installing and using Office 365 Click to run (which is how all will install unless you use an enterprise edition or buy a stand alone downloaded copy) *doesn’t work properly*. There's a lot of talk about how it should work, but it doesn't. At least not the way it should/could. Windows does not index BCM and Outlook doesn't recognize it as an Address Book/folder. Hopefully this saves someone some time. I've searched extensively for answers and invested a good 30 hours into this mess and finally went back to Office 2010 (works perfectly). If you have 2013 installed and are wondering why you can't search BCM contacts in the "Search People" box (Find a Contact) in 2010, or if you double click an email address in an email and it doesn't open the BCM contact properties page with the option to open the BCM contact, it's because you have Office 365 installed.
Bottom line - if you want a fully functioning BCM you can't use Office 365, unless it's an Enterprise standalone copy that installs MSI *not CTR*.
Bottom line - if you want a fully functioning BCM you can't use Office 365, unless it's an Enterprise standalone copy that installs MSI *not CTR*.