The menu items in MenuTagMultiselectWidget could theoretically support icons but does not in the current implementation. Example code which I expect to generate menu items with icons:

var widget =  new OO.ui.MenuTagMultiselectWidget( {
    options: [
        {
            data: 'user',
            label: ' User Namespace',
            icon: 'userAvatar'
        }
    ]
} );

A workaround, for now, is to subclass MenuTagMultiselectWidget and either
a) override createMenuOptionWidget (with a lookup mechanism data => icon)
b) override both addOptions and createMenuOptionWidget to use the full extent of available menu item config options