Sure they can.
While the vast majority of all AC motors are induction motors, brushed AC motors certainly exist, and are used in professional grade hairdryers, electric mixers, electric hand drills, etc. They're called universal AC motors and are built much the same as their DC counterpart, but have slight changes (winding ratios, laminations) for efficiency sake.
Speed control of such a motor is easy as its speed is a function of applied voltage. So use a rheostat or variable autotransformer...