Galactic cosmic rays are believed to be accelerated at supernova remnant shocks. Though very popular and robust, this conjecture still needs a conclusive proof. The strongest support to this idea is probably the fact that supernova remnants are observed in gamma-rays, which are indeed expected as the result of the hadronic interactions between the cosmic rays accelerated at the shock and the ambient gas. However, also leptonic processes can, in most cases, explain the observed gamma-ray emission. This implies that the detections in gamma-rays do not necessarily mean that supernova remnants accelerate cosmic ray protons. To overcome this degeneracy, the multiwavelength emission (from radio to gamma-rays) from individual supernova remnants has been studied and in a few cases it has been possible to ascribe the gamma-ray emission to one of the two processes (hadronic or leptonic). Here, we adopt a different approach and, instead of a case-by-case study we aim for a population study and we compute the number of supernova remnants which are expected to be seen in TeV gamma-rays above a given flux under the assumption that these objects indeed are the sources of cosmic rays. The predictions found here match well with current observational results, thus providing a novel consistency check for the supernova remnant paradigm for the origin of Galactic cosmic rays. Moreover, hints are presented for the fact that particle spectra significantly steeper than E-2 are produced at supernova remnants. Finally, we expect that several of the supernova remnants detected by HESS in the survey of the Galactic plane should exhibit a gamma-ray emission dominated by hadronic processes (i.e. neutral-pion decay). The fraction of the detected remnants for which the leptonic emission dominates over the hadronic one depends on the assumed values of the physical parameters (especially the magnetic field strength at the shock) and can be as high as roughly a half.