It has a 24-pin connector on the motherboard, sure. But you can put just 20-pins in. Most system builds from Gateway, Dell, HP, etc. that use on-board graphics will only use 20-pins.
The problem with the adapter is you're only splitting up power across more pins on the board, but the load on each lead before the adapter is still exactly the same. So you're not splitting up and reducing load, but you are actually increasing resistance.
But now I have to ask you this..... what's the rest of the build?
If your current PSU is so old that it doesn't even have a 24-pin for the motherboard, it probably doesn't have enough for your other components. Unless you tell me you're using a GeForce 9400 GT for a graphics card, or a Radeon HD 4550 I would say you should be buying a new power supply... not just an adapter.