Source power with 2 V and LED with forward voltage of 2 V
No, it would not damage your led. The forward voltage of a led is, the voltage at which the led 'conducts' the maximum current it can handle. Since diodes have a (exponential) curve, the current though a diode depends on the voltage across it.

So if you give the led 2V, it will use only 20mA. However if the voltage goes to e.g. 2.1V the current might be 25mA (since the curve is exponential), which is a bit too high, and will reduce the leds lifespan.

So for safely I'd add some resistors. E.g. a 10Ohm resistor will limit the current to 20mA max, as long as the voltage doesn't go over 2.2V

PS note that led Christmas lights use the same method to limit current, without a single resistor. I have here a 24v string of leds, grouped into 10 leds connected in series. So the voltage across each led is 2.4V. They are white leds, so they probably have a forward voltage of around 3.2v. But since they only get 2.4v, they will probably use only 5mA or less.