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Yes, Ben does push the button.

I believe you mean in the Hurleycentric episode "Dave," 2.18, when Ben tells Locke that in the previous episode, "Lockdown," 2.17, he had not had the chance to enter the #s in time, and after seeing hieroglyphs images and hearing "System Failure," and some magnetic effects, the counter reset to 108 00 by itself.

We know Ben entered the #s because, well, we know what happens when you don't, "Live Together, Die Alone, Part 2," 2.24. We know Ben entered the #s too late, after the sequence ended, because of his description of the hieroglyphs, magnetic effects, etc, that unchecked, tear the Swan Station apart until Desmond uses his key to dissipate the energies.