Jumping in here from experience: it was pretty weird to get proper hash routing (with back-button support) working with OOUI. Not impossible, but not incredibly obvious from the get-go since you still register routes via MFE, but also have to override teardowns of dialogs (the only component I'm familiar with, anyways). A quick example of some needed workarounds from the ZeroOverlay module in the ZeroBanner extension (sorry for no syntax highlighting):

45 ProcessDialog.prototype.getTeardownProcess = function ( data ) {
46     // Parent method
47     return ProcessDialog.super.prototype.getTeardownProcess.call( this, data )
48         .first( function () {
49             if ( window.location.hash.indexOf('#/zerosite') > -1 ||
50                  window.location.hash.indexOf('#/zerofile') > -1 ) {
51                 history.replaceState('', document.title, window.location.pathname + location.search);
52             }
53         }, this );

54 };