No. The 4th Amendment requires government action. Burdeau v. McDowell, 256 U.S. 465 (1921); Walter v. United States, 477 U.S. 649 (1980).
A search or seizure carried out by a private individual, even if it is unreasonable, does not implicate the Fourth Amendment. United States v. Jacobsen, 466 U.S. 109, 113 (1984).
But, will information provided to the government by private businesses be acted upon properly? If a business owner points to a customer and cries to a government agent, "he's got a gun!!", do you think the agent is going to honor freedom from search and seizure?