Can I use a 120V power cord on a 208V 3-phase circuit?
You'll be fine.  

What's happening is that 208V 3-phase is "wye" configuration.  Think the flux capacitor from back to the future. The center is the neutral.  Each leg of the Y is 120V from neutral.  

The C13 socket on the PDU is giving you one leg and neutral, for 120V.  

Why is it 208V?  Remember your geometry? Draw a perfect wye, then connect the corners and you have a perfect triangle.  If center to corner is 120, then corner to corner must be that times sqrt(3) or 208.