Over the last year I have noticed that any Tahoe police/law enforcement vehicle I have seen does not have the hitch in the rear bumper cross member. I am not sure at what point GM went to a specific bumper for the police trucks but you may want to verify there is a hitch.
Being a 2009, is it the 4 speed or late enough it has the 6 speed? What axle ratio?
Your towing success will depend on what you put in the truck while towing. If you are loading with 6 people and luggage you may not like how it tows. Two people and you may do okay.