Do I need a current limiting resistor when powering an LED below its forward voltage?
Have you tested the two alkaline batteries?  I'd bet they are slightly above 1.5V each, bringing your total voltage up to the LED forward voltage.   However, when the LED starts conducting, its low impedance pulls the battery voltage down slightly, and the battery itself acts as the current limiting resistor.

As to the second part of your question, I can't say whether its always better to add the resistor and use more cells.  If you're making an LED throwie, then it definitely isn't.  If you want a consistant runtime that doesn't rely on hitting a bullseye between battery voltage and current draw, then probably.