Powering a LED off a 1,2 volt rechargeable battery
No, because when the supply is below the LED's forward voltage only a very small amount of current (hundreds of microamps, if that) will be able to flow; if the LED is visible at all it will be very dim.

The danger with too high a voltage is that the amount of current that is allowed to flow will be too high for the LED's power handling and the semiconductor will melt/blow up, but this is not a problem is the voltage if too low to allow much current at all.