You'll be assigned to a unit at basic training, then a different one at AIT, although it's a little different from what you'll experience after AIT.
If you value your knife, I would leave it at home, because even once in AIT, the Army is going to give you a long list of things you can't have on your person or even in your quarters, and they love making examples of people. When my wife was in AIT at Fort Sam Houston, food wasn't even allowed in rooms. Nothing but water, actually. That even applied to prior service personnel who were there for training events. However, some of the restrictions may have been unique to that base, so a recruiter probably isn't going to have a concrete answer.