I took my bag to the interview with me on three different occasions. The majority of schools expect that several students (depending on interview group size) will have a bag with them.
It simply isn't feasible for everybody to leave their bags at the hotel, and then go back to the hotel before going to the airport.
I explained to each of the admissions officers that I brought my bag with me so I wouldn't have to go back to the hotel, which left me with more time to observe in the clinics and attend classes with the students. Each of the admissions officers agreed that since I payed gobs of money to attend the interview, spending as much time as I could as the school was the best option, and they mentioned that they wished other applicants would spend more time at the school looking around and participating in clinics.
If you verbally explain this to them, not only will they not have bad impressions, but they'll move you to the top of their potential matriculants list. Trust me, nobody cares if you bring an overnight bag.