Some do, some do not. Smart managers will not do this if people are not taking advanage of the property, as it is an inducement to return.
Nonetheless, I have been refused at one property at least - a standard sized carry-on at the DoubleTree SFO, where the so-called HHonors Manager called the bell staff and said "I have a guest who wants to leave baggage; you don't have room for any, do you?" Uh, no, of course not...
Congratulations, and thanks from someone who has stayed probably close to a hundred times over the years. (This person I think has left recently, no loss - such a rigid personality I think she is positively frangible.)