Can I Connect a DC Motor to the Transistor's Emitter?

If the motor is connected to the emitter (and ground), the voltage could be that low.
Also, if you use a battery for the motor, it is best to connect the motor to the collector (and battery plus).

You can try for yourself, and measure the voltages.
But use a resistor of about 1k at the output of the Arduino. That way the Arduino output is protected in case you connect something wrong.