Inventory Commitment Preference - Default Warehouse?

I'm trying to determine if the Inventory Commitment Preference will work for my purposes.  Each of our customers is set up with a default branch, either A or B, based on geography.

Can the preference, either basic or advanced, be set up so that the default branch is checked first?  If the default branch cannot fulfill one or more lines, those are shipped from the opposite branch.

At this point, I think we would be using an All Customers/All Items hierarchy.