## Yes and No ##

See [Katz v. United States, 389 U.S. 347, 351 (1967)][1]:

>What a person knowingly exposes to the public, even in his home or office, is not a subject of Fourth Amendment protection. But what he seeks to preserve as private, even in an area accessible to the public, may be constitutionally protected.

The glass has clearly been "knowingly exposed" and if that glass was on the normal methods of examination by the officer (sight, smell etc.) evidence of a crime then it would be able to be used as evidence. However, any DNA on that glass is not "knowingly exploded" - finding the DNA requires a laboratory, specialised equipment and trained technicians.

  [1]: https://www.law.cornell.edu/supremecourt/text/389/347