X1 Search v8.4.1 and higher is compatible with Office 2007 and Office 2010-2016 (32-bit and 64-bit). This includes Outlook and Exchange 365.
X1 Search is able to index Outlook 365 emails that are stored in the cloud only, however if the machine is not connected to the Internet when searching you will not have access to previews as X1 Search is not able to pull the preview from the cloud unless connected to the Internet.
If you wish to have your hosted Exchange run in cached mode with the OST stored locally, you will have access to previews regardless of your Internet connection status.
This Microsoft Office Online article goes through turning on cached exchange mode: https://support.office.com/en-us/article/Turn-on-Cached-Exchange-Mode-7885af08-9a60-4ec3-850a-e221c1ed0c1c
Once in cached mode, the OST location is by default in C:\Users\Username\AppData\Local\Microsoft\Outlook