Yes. The United States Supreme Court has held that a person has no expectation of privacy in abandoned property (Abel v. U.S., 362 U.S. 217 [1960]).  Property is abandoned when a person has “voluntarily discarded, left behind[,] or otherwise relinquished his interest in the property in question so that he could no longer retain a reasonable expectation of privacy with regard to it at the time of the search (United States v. Colbert, 474 F.2d 174, 176 [5th Cir. 1973]), accord United States v. Masiello, 491 F. Supp. 1154 [D. S.C. 1980]).
In U.S. v. Walker, the District Court of Maryland found that a bag containing trash and other material, left by the roadside by a suspect, was abandoned under this standard and that the suspect had no reasonable expectation of privacy that would prevent government investigators inspecting the bag without a warrant (624 F. Supp. 99 [D. Md. 1985]).  In 1988, the United States Supreme Court held that a person had no reasonable expectation of privacy in trash placed in opaque bags at the curbside for collection by a garbage collector (California v. Greenwood, 486 U.S. 35 [1988]).  Accordingly, collection of the trash by government officials without a warrant or the suspect’s consent was permissible (Id).  Under this precedent, the City and its agents are legally entitled to inspect materials left at the curb for collection by Republic Services as trash and recyclables.