I don't quite understand what you are describing, but the sense wire is for the PSU to get a more accurate feedback of the voltage at the output end.
Imagine you are drawing 1A from the 3.3V rail, and you have a very crappy cable from PSU to motherboard, with 0.1 ohm resistance.
The voltage you'll see on the output will be 3.2V, due to 0.1V (1A * 0.1 ohm) drop. The PSU wants to know that so it can increase its voltage output to 3.4V instead, so you can actually get 3.3V on the output side.
So it needs to know the voltage after the drop, and that's through the sense wire, which should carry negligible current (so it has no significant voltage drop of its own).
It's a deceptively simple mechanism that can and often do go very wrong. The problem is when the PSU increases its output, due to capacitance and inductances in the wires, it will take some time for it to have an effect on the actual output side (motherboard), and then it will take some more time for that increase to go back up to the PSU through the sense wire.
If the delay is just right, the output rail can go into oscillation.
For example, the PSU sees that the output voltage is slightly low, so it increases its output. But the increase takes some time to come back, and in the mean time the PSU will keep increasing output voltage. By the time it sees 3.3V on the sense wire and stops increasing voltage output, the output may already be at 3.5V (overshoot). Some time later, the PSU sees that, and start decreasing the output voltage, but the delay messes things up again, and it goes down to 3.1V (undershoot) before it sees 3.3V on the sense wire. Then it increases again and the cycle continues.
If the second overshoot goes higher than the first (say to 3.6V), the system is unstable, and the magnitude of the oscillation will keep increasing until something blows up.
If the second overshoot is lower, that's a lot better, because it will eventually settle on 3.3V. It's not ideal, though, because that means every time the load changes, the voltage will ring for a bit before settling.
Amplifier stability is one of the all time hardest problems in electronics engineering, and people designing PSUs need to keep that in mind at all times. They designed the PSU so that it won't oscillate with the given length and type of wires and connectors (since changing length or type of the wires will result in different capacitance, resistance, and inductance, and hence signal delay).
Messing with the feedback signal is always risky, because you'd have to do a lot of crazy calculations to make sure the amplifier will still be stable with new feedback characteristics, and for that you need the internal design of the PSU (and deep electronics engineering knowledge).
If you rewire it with different characteristics, it will PROBABLY still work 99% of the time, because they likely designed some safety margins into the PSU, so that it can still be stable with slightly different feedback characteristics. But you'll never know for sure anymore. There is a very tiny chance that it won't be stable anymore at very high current or very low current, or certain kinds of load characteristics.