Yes, but the LED will be dimmer.
Calculate it for yourself:
1. find the voltage across the resistor, this is the difference from one end to the other so it is the supply voltage minus the LED voltage. Call it "Vres".
2. the power it dissipates (in Watts) is Vres Squared divided by the resistance (V*V)/R.
You can get the LED voltage (called Vf) from its data sheet or measure it with a meter. Note that it stays fairly constant when the current changes.
Looking at Prairiedog's calculation, Vres is 13.8 - 1.8 = 12V. 12 squared is 144. The power it dissipates is therefore 144/510 = 0.282W. From 12V it works out to b 0.204W.
The same power is always dissipated no matter how high the resistors power rating but higher rated ones generally are physically bigger so the heat is easier to dissipate and they run cooler. Those tiny ones provided with Chinese LEDs are usually rated at 0.125W (1/8W) which is why they get so hot when you push them beyond their rating.
Brian.