I'll expand on my 'no'.
I would like to point out that Dwarf Fortress is already in 3D (having the Z axis and all), so that can't possibly be the point of the suggestion. So I'm guessing that the suggestion of using CUBE is about the graphics.
Dwarf Fortress doesn't need 'graphics'. One of the reasons that DF is so incredibly awesome is that it's a game that focuses on gameplay. It's all about playing the game, and adding things the complement, accentuate, and enhance that gameplay. And you can argue all you want, but graphics are not gameplay. Sure, they may be sexy, but are they really needed? Would you rather a game that's great to play or good to look at? You can rarely find both, and the vast majority of games these days sacrifice being fun to play to look shiny (and all shades of brown and grey)
Someone will of course say that with 'better' graphics then DF will be more accessible and attract more people. And it will - but will they stick around? No. You may be attracted to a game because of the graphics, but you play because of the gameplay. All the media-release press-package photoshopped screenshots in the world will be instantly forgotten as soon as you play the game and discover what it's actually like to play. Case in point - Halo 3. Wonderful looking game, gorgeous screenshots - and absolutely average gameplay.
DF is the game that you wish developers made if they had invested their money in gameplay instead of licensing the newest whiz-bang graphics engine and coding nothing but graphic shaders.
And what if Toady decided to shift the engine to CUBE (or Ogre or Irrilict, or whatever you want to throw around)? It would be a nightmare. The vast majority of the engine would have to be re-written, and I can speak from experience that coding something for 3D is far more complex and time-consuming than 2D programming. If Toady dedicated all his time to just making DF 3D, then we wouldn't see another release with any gameplay features for at least[i/] 2 years, I'd guess. Now, I know Toady's a math genius and all so he'd be comfortable with matrices and quantarions out the wazoo, but like he's said before, he's not a trained coder, and it takes packs of trained coders years to create a working 3D engine.And then what? Well, there's all the content. Everything has to be modelled in 3D, have their textures drawn, the shader code written. Have a look at the default content that comes with DF. Hundreds of unique creatures, plants, workshops, clothing, and perhaps the most diverse and comprehensive terrain and environment system known to gaming. Now, a decent modeller will take about 2 weeks to model a single character. Animation for the basics (walking, running, idling, attacking) may take another week. Texturing another week on top of that. Multiply that by a few hundred and you've got transferring content alone taking a few years.
I could go on and on, but really...