Use Outlook from Office 365 to connect to another email server provider

We are in the process of migrating our emails from a third-party company to Office 365.  In the mean time, we are trying to set up some workstations with Windows 10 and Office 2016.  We decided to use one of our Office 365 licenses to download Office to one of these Windows 10 workstations.  Before we are ready for the migration, we would like to set up Outlook 2016 with our current third-party email company as they currently still manage all of our emails for our company domain.  When we try to set up the email account in Outlook, it appears to recognize the email server because we don't get any error that it connects.  But when we open Outlook 2016, it's not showing any emails.  Are we allowed to set up the Outlook 2016 with got from Office 365 to connect to another email service until we are ready to migrate to Office 365?  If so, is there a process for it?  We're confused why it seems to connect, but then we don't get any emails.  Hopefully I didn't confuse anyone, but please ask any questions you may have.