If I drive an LED whose forward voltage is 2V with a source that's 3.3V limited to 20ma, will I harm the LED?
Unless the output was designed specifically as a current limiter, the source limit specified on the datasheet doesn't mean "I will helpfully keep the current at this level for you," it means "you had better keep the current below this level or bad things will happen."  You need resistors on each output.