The manifestation of extreme solar proton events (SPEs) in Beryllium-10 (10Be) ice core data contains valuable information about the strength and incidence of SPEs or local characteristics of the atmosphere. To extract this information, the signals of enhanced production of cosmogenic 10Be due to the SPEs have to be detected, hence distinguished from the variability of the background production by galactic cosmic rays (GCRs). Here, we study the transport and deposition of 10Be from GCRs, using the ECHAM/MESSy Atmospheric Chemistry climate model, and discuss the detectability of extreme SPEs (similar to the CE 774/775 SPE) in 10Be ice core data depending on the ice core location, seasonal appearance of the SPE, atmospheric aerosol size distribution and phase of the 11-year solar cycle. We find that sedimentation can be a major deposition mechanism of GCR generated 10Be, especially at high latitudes, depending on the aerosols to which 10Be attaches after production. The comparison of our results to four ice core records of 10Be from Greenland and Antarctica shows good agreement for both 10Be from GCRs and solar energetic particles (SEP). From our results we deduce that the location of detection and the season of occurrence of the SPE have a considerable effect on its detectability, as well as the aerosol size distribution the produced cosmogenic nuclides meet in the atmosphere. Furthermore, we find that SPEs occurring in the phase of highest activity during the 11-year solar cycle are more detectable than SPEs that arise in the phase of lowest activity.