Bypass capacitor before or after circuit, does it matter?
It makes no difference.

What matters is (mainly) the loop area from the positive terminal on the IC, through the IC to its ground pin, through copper to the negative terminal of the capacitor, through the capacitor, and then through copper to the positive terminal of the IC.


  In both cases, assuming the capacitor is very close to the circuit, it will absorb the noise caused by the long supply lines ...


The noise isn't caused by the supply lines, it's caused by the switching currents from the IC (which you correctly model with a current source) and the impedance of the network providing power. You are correct that it doesn't matter "which side" of the IC the capacitor is located, if it provides a low-impedance path for the switching currents it will prevent them from producing voltage variation on the supply net.