Hello,
Let me paint a picture, there are two companies (parent and child) with their own individual Office 365 tenants and a bi-directional transitive forest trust between AD schema's on premise. They want to synchronise the GAL between tenants/forests so that Outlook and Lync users receive up to date information about contact information, availability etc. Office 365 is used for Exchange, SharePoint and OneDrive with Lync being on premise.
Now I understand you can't synchronise between the tenants, but does having a trust between the two AD schema's make any difference? For example having two FIM infrastructures replicating between each other?