No. The Motorola charger uses a five pin mini-USB connector, the charger is on the other end, and inside the charger there are connections between the signals that the phone detects to determine that it's a Motorola charger.
The five pin mini-USB to 4 pin USB A cable used to plug the phone into a PC will only charge the phone when the Motorola Phone Tools software is present.
If you use a power-only USB cable (no signal lines, just power and ground) which do exist, then the phone won't charge from a USB port because the phone will know that it's not plugged into a Motorola charger.
Similarly if you use a cable with all the signal lines, but plug it into a power-only USB supply (12VDC to 5VDC USB cigarette lighter adapter,
110VAC to 5VDC USB adapter, or the USB power port on many 12VDC to 110VAC inverters) it won't charge the phone because the phone will know it's not plugged into a Motorola charger. You could build a special cable that simulates what's present inside the charger to get around this, or you could modify the phone to get around this (people have done both).