It may be possible but you would lose, not just hide, the Ribbon. In Word 2013 you can double-click on a Ribbon Tab and hide/show the Ribbon. The tabs will still be displayed. To me, this is the maximum practical method for gaining screen real estate. The Auto-Hide option hides the Ribbon and Tabs, but also hides the QAT.

Otherwise, you could use the AutoHide option. That can be selected in the top right corner of the window. It has an icon of a rectangle with an up-pointing arrow in it. The AutoHide option hides both the Ribbon and QAT but will display both if you move your pointer to the top of the Window. Note, this option first became available with Word 2013.

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