@kevink it does work under certain instances. It will depend on the individual logic board and the damage to the solder joints as well as the chip itself. What will become important is to why this happens and why this is an individual logicboard issue. Here is a quick and dirty explanation.
You most likely have issues with your GPU processor. It is a flip chip design and the issue could be the solder bumps between the IC and the substrate. It is not always a failure of the solder balls which connect the Flip Chip BGA package to the motherboard. It does happen and you can see why on here More commonly however is that the failure is due to the chip design itself.
As you can see the "bumps' are what actually connects the die to the substrate to make the chip complete. If these bumps fail, the die does no longer make contact with the substrate and thus no contact with the circuit board. The chip has failed.
Here you can see the space where the bump has failed and no longer makes contact. We are talking microns of space here. So a bit of pressure on the top of the die potentially close the gap. Same with a reflow, it may allow some of material from the bump to reshape and starting to make contact again. The heating of cooling of the chip during use is what will eventually cause it to fail again. That explains the importance of good thermal paste, a good clean running fan as well as good air circulation.
A reball done properly can buy you time and may outlast your PS3 altogether or it may fail tomorrow.. There are just no guarantees.