Is it fine to reuse the Quick Order view in one of our own screens? We're adding the Quick Order view as a child view in one of our views like so:

this.childViews = {
    'Quick.Order': function() {
        return new QuickOrderView({
            openQuickOrder: false
        });
    }
}

And then referencing in the View's tpl like so:

<div data-view="Quick.Order"></div>

P.S.: QuickOrderView was added as a dependency to our view as 'QuickOrder.View'.

It is not allowed in an extension, no. It is a core module that is not on our list of allowed modules.

Understandable, thanks for confirming.