Nope. The SS scene seems to demonstrate that she doesn't know Bruce Wayne, but that's a separate issue from knowing that Batman and Matches are one and the same (particularly since Matches is a working ID, and therefore not just a sign of extreme trust, but outright essential to the basic functioning of the crimefighting partnership).
And it's cleanly out-of-continuity anyway, since BG:Y1 established that Babs got brought into the inner circle within, like, a week of putting on the costume. So even if it did contradict the fanwank here (which it doesn't, but if it did), that contradiction would be retconned out by virtue of Y1 as well.