It looks like it can or is maybe learning to. Two guys were standing on the sidewalk and it just murdered one with its antlers or possibly a head-butt. It was about to go for the second but suddenly re-spawned in the airport for some reason.

The animals in GTA:V do have attacks (sharks, dogs and mountain cats bite, etc). If you use a mod to play as an animal it becomes your melee attack.

Modding support in the GTA series is excellent, and has spawned a large community. It's refreshing to see as locked down games with DLC sold for extra are becoming the norm, with a few notable exceptions such as the Fallout series.

I've been having a lot of fun using a police mod where you can spawn FIB elite units that are allies. It'd be great to command an animal army as well!