Nope, DNF is powered by an enhanced edition of Unreal Engine 2, which was first used for UT 2003 and Unreal II. And those games were released respectively fall 2002 and early 2003 ... this is 1.5 - 2 years before Doom 3
But as I have already said on another topic, their improvements and the full support of DX9 put the engine around the same level as id Tech 4.