If you keep your modified imagemagick a separate program from the server that interacts with users (and don't e.g. exchange complex internal datastructures over

If you keep your modified imagemagick a separate program from the server that interacts with users (and don't e.g. exchange complex internal datastructures over IPC between imagemagick and the server) then it seems fine. If you add network interactivity directly to imagemagick then no. I wouldn't worry too much about this case in practice because there are very few programs that choose the AGPL and don't have network interactivity.