Expense or InvoiceConnect can utilize Intacct's dimension auto-fill capability. The one gotcha is to uncheck the "Enable override of auto-filled objects" checkbox on the known dimension's object properties in order to allow this to work.
In Concur Intacct Project's are assigned to expense line items. You need those projects to auto-fill the class assigned on each project. In order to do this, you need to uncheck the checkbox on the Project object properties page (see the attachment).