Yes.

Since its very earliest development phase, the physics model in Halo has been described as being among the most advanced ever put in a video game. Most parts of the game, from falling shells to the movement of planets in the Halo solar system, will be handled by the same global physics model.

In an interview back in 1999, then-Bungie employee Nathan Bitner described Halo's physics this way:

Our jeep has 4-wheel suspension! Each wheel is independent! The antenna and driver bounce around as they would in real life! Inverse kinematics have the driver gripping the steering wheel and stick shift as they would in real life! I guarantee you would want to buy Halo if it was just a racing game and there weren't even any guns. That's how amazing the vehicles are going to be ... and how they are going to FEEL. And there will be PLENTY of vehicles and weapons to hold your attention span. I wouldn't be surprised to find players using inferior weapons or vehicles just because they're so much fun to use.

The behavior of vehicles in the various demonstration movies of Halo has been quite impressive.