We investigate the observable effects of feedback from active galactic nuclei (AGN) on non-thermal components of the intracluster medium (ICM). We have modelled feedback from AGN in cosmological simulations with the adaptive mesh refinement code ENZO, investigating three types of feedback that are sometimes called quasar, jet and radio mode. Using a small set of galaxy clusters simulated at high resolution, we model the injection and evolution of cosmic rays, as well as their effects on the thermal plasma. By comparing both the profiles of thermal gas to observed profiles from the ACCEPT sample and the secondary gamma-ray emission to the available upper limits from Fermi, we discuss how the combined analysis of these two observables can constrain the energetics and mechanisms of feedback models in clusters. Those modes of AGN feedback that provide a good match to X-ray observations yield a gamma-ray luminosity resulting from secondary cosmic rays that is about 10 times below the available upper limits from Fermi. Moreover, we investigate the injection of turbulent motions into the ICM from AGN, and the detectability of these motions via the analysis of line broadening of the Fe XXIII line. In the near future, deeper observations/upper limits of non-thermal emissions from galaxy clusters will yield stringent constraints on the energetics and modes of AGN feedback, even at early cosmic epochs.