Context. Recent observations of unexpected structures in the Galactic cosmic ray (GCR) spectrum and composition, as well as growing evidence for episodes of intense dynamical activity in the inner regions of the Galaxy, call for an evaluation of the high-energy particle acceleration associated with such activity and its potential impact on the global GCR phenomenology. Aims. We investigate whether particles accelerated during high-power episodes around the Galactic centre can account for a significant fraction of the observed GCRs, or, conversely, what constraints can be derived regarding their Galactic transport if their contributions are negligible. Methods. Particle transport in the Galaxy is described with a two-zone analytical model. We solved for the contribution of a Galactic centre cosmic-Ray (GCCR) source using Green functions and Bessel expansion, and discussed the required injection power for these GCCRs to influence the global GCR phenomenology at Earth. Results. We find that, with standard parameters for particle propagation in the galactic disk and halo, the GCCRs can make a significant or even dominant contribution to the total CR flux observed at Earth. Depending on the parameters, such a source can account for both the observed proton flux and boron-to-carbon ratio (in the case of a Kraichnan-like scaling of the diffusion coefficient), or potentially produce spectral and composition features. Conclusions. Our results show that the contribution of GCCRs cannot be neglected a priori, and that they can influence the global GCR phenomenology significantly, thereby calling for a reassessement of the standard inferences from a scenario where GCRs are entirely dominated by a single type of sources distributed throughout the Galactic disk.