Why would it? The only thing that would happen, as st0x said, is you probably won't rank for anything important and because it's cloned everywhere, someone else (likely DMOZ itself or the Google variant thereof) will rank ahead of you, all other things being equal.
Good for that site I guess, but given that same content has been cloned so many times over I doubt the pages would show up in SERPs. Mostly like all the pages are in the supplemental index and keep some of the other pages on the site ranking as well as they could.
If Google was going to show a page in their results that's an exact match for a DMOZ page, which page do they think they'll show? My money is on the original page at DMOZ.
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