Göker uses a single MKE GDF-003(single version of Korkut basically), so fire rate should be similar to that, 550-600 RPM. Unsure if Korhan comes with MKE's 35mm revolver gun or not so can't comment.
Takes less space, but I fear even with ATOM its fire rate is too slow for quick bursts. Makes sense for C-RAM fire against free dropping mortars or slow moving drones as well as base defence in Göker, but this system would also be tasked with VSHORAD duties against fast moving PGMs like cruise missiles and turbojet drones.