Actually, none of this is all that simple in induction motors, there are very complex relationships involved between applied voltage, load and motor design. You actually can only make very grossly generalized assumptions about what will happen to a motor under low voltage conditions and even then, only if you first define what you mean by "low".
For example, at great risk of dragging them out of the sewer where they belong, the so called "Nola Circuit motor energy savers" do in fact reduce the voltage to the motor, which does in fact reduce the CURRENT drawn by the motor (just NOT THE ENERGY it consumes by as much as they claim). Also think about this; if current in a motor is supposed to increase as voltage decreases, why does a "Reduced Voltage Starter" reduce the current? That's why I say it is too complex to throw blanket statements at, other than to say that IN GENERAL, running a motor under full load at a voltage significantly lower than the design voltage will usually result in an increase in current.