No.
You will not be able to migrate a customer from hosted Exchange Server such as Intermedia to Office 365. The reason is that Exchange Migrator connects to you Active Directory/Domain Controller to access a list of the Exchange mailboxes you will be able to migrate. Hosted Exchange Servers like Intermedia do not have a dedicated AD/Domain controller and as a result there is not way to access the list of mailboxes/users directly from the Active Directory.