Yes, assigning Broadcast.WepGrFoc to a weapon tells the program that the weapon has greater weapon focus - therefore give it the +1.
Actually, is there any other feat that requires this as a prereq? If there's no need to assign a broadcast tag for prereqs, and there's no reason to assign it so that another script can find it and use it, just don't assign a Broadcast tag. Delete the whole third section ("~assign the appropriate tag..." of your script and the second to last line ("result = field[fChosen].chosen.assign...").
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