Only if it is marked at 120. For example, the power supply on laptop power supplies is designed to work worldwide so its cord is also rated for the higher voltage.
The danger here is very small and the thing that comes to mind is leakage to the surface. Run your equipment and touch the wire to see if you feel electricity leaking to outside of it. I doubt that you will feel anything. But if you do, it is not a good sign. The other issue which you must avoid is total power through the cable. At 240 volt and the same amps, you can draw twice as much power through the same cable. That causes double the losses in the cable, potentially compromising its insulation. Worse yet, the fuse/breaker in the house will not protect it against shorts and risk of fire. I suspect your gear doesn't pull twice as much power so this is not an issue in this situation.
Mind you, many times the cable is also good for 240 but manufacturer saw no reason to test it at higher specs. This is why I said risks are very low.
BTW, IEC spec goes up to 250 volts. Why not use a cable rated at higher voltage to start? Here is a random one that came up in search:
http://www.costcentral.com/proddetail/Eaton_Corporation_EATON_ePDU/0100028/Y71595/