Mark is completely correct. I'll add a little to it. Acoustical summing at dead center in a near field should add 3dB to the sound energy over hard Right or Left, when patched directly (not using a pan pot).
The general purpose of the 'panning law' is to compensate for this acoustical summing when panning through center. When done right, as you pan your sound, it will keep the same apparent volume across the soundfield.
This phenomenon does not always behave perfectly, nor is it what mixers always want, so some analog and digital panners use different panning laws; say -5db down at the center, or different degrees of taper across the pan.
Under the circumstances you describe, your last sentence, "If nothing special is done..." is usually going to be untrue. Commonly, different panning laws only become an issue when the mixer needs to make a 'standardized' format conversion without remixing a new printmaster...as when turning an LCR stem into a stereo pair, for instance.