Will it hurt a 4.8 volt DC electric motor if you put 4.5 or lower volts on it?

No. Varying a DC motor's voltage will vary its speed. If your motor is rated for 1000 rpm at 4.8 volts, running it on 4.5 volts should produce something in the area of 937 rpm. It shouldn't be a very noticeable difference, unless the voltage is much lower than the rating.