Is The Safe In Hotels Rooms Secure To Dump All My Cash And Passport?

Planning my first trip to AC and read about the pickpockets etc, also been told its not a good idea to carry around more cash than I need for the day, I was wondering if the safe in the room is secure? I'll be bringing cash not travellers cheques, is it cool to dump it in there with my passport or what you do from a security point of view? Use the atm and swallow the charge from your bank?

Thanks