On a touch screen using Win 8 Metro apps then no, you would not need to have a mouse as the apps there are designed for touch. However, if you run standard desktop apps which aren't designed for touch, then it can be difficult (but not impossible) to use them without a mouse
I have a Touchscreen computer running Windows 8.1.
I have quite old legacy software which all can be touch operated.on the desktop. As said, it can be difficult to touch a small text item in, for example, a drop down menu. But they work. Admittedly, I have quite a large screen