Hi Mark:
Running a wire under a BGA is possible, however if you plan to mount the BGA over the wire you would want to make sure that the wire insulation will withstand the heat of the reflow temperature.
A more reliable way would be to lay a trace between the pads and encapsulate the trace in a high temp epoxy or solder mask.
Precision PCB Services,Inc. performs modifications of this type as intricate as drilling our BGA via's, routing trace through the board and adding pads and circuitry under the BGA package. Even on micro bga.
Go to: www.pcb-repair.com for more info.
Regards, Dennis
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