Of course it is in the "game" sense. It handles X, Y, and Z axes in game on mobs and the player, although it is selective in which mobs get the "Z treatment". Monsters are infinitely tall, projectiles aren't. It's not a limitation of the engine as much as it was a design choice, as Y-shearing was too ugly in Carmack's opinion, so it was removed in favor of a very forgiving auto-aim.

Nothing's stopping someone from adding code to render 3D models or "portals" in the game, and in fact it has already been done, with no 3D acceleration needed.