Jumping it would send power into both sides of the BCM whenever the switch is "on". That's not usually a good thing. As flaky as the GM BCM's are, I wouldn't put power into both sides of the BCM on any circuit.
By bypassing the BCM disconnecting both wires (or cutting) and hooking them together, you eliminate the BCM and wire the Fog Light Relay control strictly off of the 12V output from the switch. HOWEVER, having not explored this circuit myself, I would first test the input and output voltage on the circuit at the BCM to ensure that both Voltages match when the fog lights are "on". If the voltages match, I'd start the surgery. Be sure to only cut the wires several inches away from the BCM so that if it does not perform as advertised, you can rebuild the original circuit.
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