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The NAV integration with CRM is handled completely in NAV. So you'll likely want the US company and the EU company to have completely separate integrations with CRM. For most integration needs, this should work fine.
When a change is made in a record in US company, the NAV connector there will push the change to CRM. The NAV connector for the EU company will see the changed record in CRM and will pull the changes into the EU company. And of course the same would work in reverse when a record is first modified in the EU company. When a record is first modified in CRM, then both the EU and the US companies will see the change and pull the change to their own companies.
It's important to note that the tutorials of how to setup the NAV connector and many of the "Click this button to synchronize all your records" are more for demo purposes than real-life. Be prepared to do a lot of playing with sandbox companies to truly understand what is happening. You can also check out the video I did on the NAV 2016 CRM Integration--much of it probably applies to the 2017 integration. www.innovia.com/.../greg-enns
Best of luck!