The last couple of weeks I had the privilege to test a feature that has just has been announced today to be released to Microsoft Intune . Conditional access to Outlook Web App and SharePoint Online web access for mobile devices. (CA for web services like OWA and SharePoint for Windows (mobile and PC) is coming up and still in preview)
So basically when a device is not enrolled and / or not compliant Outlook Web App or SharePoint Online web access cannot be accessed via browsers on those devices. Until now this was a major hole in the conditional access story of Exchange Online and SharePoint Online.