Short answer is, yes. Dual pivots have more mechanical advantage because the lever arms are longer. So you get more compression on the rim for the same force on the brake levers. Brake shoes can also make a difference as well, and in general, more modern dual pivots, even on the low-end models will have much nicer brake shoe compounds than the brake blocks from the 1990s. So if you upgrade to dual pivots, you get the benefit of more MA. But if you also upgrade to more modern brake shoes, that's a double whammy.

You don't need to pay a lot for a brake upgrade. Check out BikeWagon.COM and the Tektro R466-E brakes. Around $25 per set. Nice brakes that stop great. I swapped out an old set of BR6400 (Older single pivot Shimano 600 Ultegra from the late 80's) and put on a set of these, and braking is dramatically better. Plus they look good too.