The current release of Esri Maps for Dynamics CRM (1.0) works with Dynamics CRM 2013, however it will not be officially certified on Dynamics CRM 2013 until the next release (1.0.1). The next release will be available later this quarter.
We can confirm Esri Location Analytics app support for Microsoft Office 365--Microsoft�??s hosted/Cloud platform for their Office suite of business and productivity apps. We currently have beta support for SharePoint Online for Office 365 with Esri Maps for SharePoint; and we currently have plans to support Office 365 with Esri Maps for Office in the second half of 2014.