Hi Oscar,
It's going to be a pain if they're required to create a MicrosoftID before they can add a their exchange-account. We don't need it. We don't want it.
What's the meaning? Why did you have to create a MicrosftID for adding the Exchange account? What's the meaning of MicrosoftID? Did you mean Windows Live account or others?
Then back to your question.
Based on my understanding, you want to sync your Exchange account contents (Mail and Calendar) for domain computer when this computer is outside of the domain network, right?
If yes, this could be done and it's default it could. Please make sure you didn't set any policy to restrict it. And then Exchange autodiscover will search this account. If it in outside network, autodiscover will obtain the external URL to sync the account.
For further help, I would like to suggest you ask in Exchange Server forum for profession help(include your Exchange Server version ect information in your post):
https://social.technet.microsoft.com/Forums/office/en-US/home?category=exchangeserver
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