Well, I would have to disagree with Irrlicht being only a graphics engine (after all there is built-in collision detection, GUI, and input handling) - however, for the purposes of this question, I will agree with hybrid.
Irrlicht is not a "game engine" per se, and as such does not integrate all that is required for game development (for example, there is no networking, no sound support, no movie clip display, etc). And physics is one of those things that is tweaked to hell and back for individual games. Most games do not need (and/or cannot afford the CPU cost of) a fully generic physics engine. Doom 3 had a cut-down, hand-coded physics engine. BloodRayne 2 hacked the buggery out of ODE. Half Life 2 had a custom wrapper around Havok. The list goes on.
My point is that what physics engine you use, and to what degree it conforms to "real physics" (i.e. what hacks & limitations you code into it) can vary wildly from game to game. As such, even if Irrlicht was a game engine, adding a physics engine to Irrlicht would only be a stopgap until you replaced it with something better for the game.
If my minor rant does not dissuade you - try the MyWorld port/distro of Irrlicht. The developer of that has integrated ODE into the engine and put the source code online.
--EK