Hi Maureen,
Regarding Compatibilty, we cant officially support syncing or integration with a file hosted on QBox. That being said, it may still work if Im understanding your setup correctly.
You have a a multi-user mode QuickBooks file with;
- One installation on a local PC, along with the Method Integration Engine
- A second QB file installed on your Laptop which then syncs to QBox
In the above scenario above, the syncing Should still take place with your QBox hosted file, but you will lose the ability to sync in real time. Any changes made to the QuickBooks file on QBox, or the Second Laptop will not be reflected in Method until the next Full-Sync occurs (typically the next day). The reason being is that Records need to be 'Flagged' as having been changed or added/updated, and Method will not know a change has taken place elsewhere until a line-by-line comparison (aka a Full Syncronization) occurs.
Another point of note: If QBox locks down the QuickBooks file while someone is accessing it, the Sync from Method > QuickBooks will not take place during this time. The Engine and the File Both need to be open and logged in on your local machine for the synchronization to occur in any capacity.
Let me know if you have any further questions! 
-Ben