The Third Circuit, sitting en banc, has split 8-6 on this in today’s United States v. Mitchell; the majority concludes that the law authorizing this practice does not violate the Fourth Amendment. The Ninth Circuit will soon consider en banc a related question, which is whether the government may collect DNA as a condition of releasing someone on bail.
Note that this has to do with testing in the absence of probable cause (or even a reasonable suspicion) that the DNA would be evidence related to a crime. Thanks to How Appealing for the pointer.