Hi Fambrough,
If you keep using the email services at Host Excelence, Outlook Web Access (OWA) on Office 365 will not be used. If you want to use the Office Web Apps on Office 365, Sharepoint Online services on Office 365 can meet your requirement.If you want to use Email services on Office 365, you need to migrate email to Office 365 and then change the MX record to point to Office 365.
For details, please refer to the link below:
E-Mail Migration Overview
http://help.outlook.com/en-us/140/ms.exch.ecp.emailmigrationstatuslearnmore.aspx
Thanks,
Aaron Yuan