Disk, audio, ... DMA is no problem for copper lists. You can either make it wait until the high priority DMA slots are done (horizontal blanking period) or just live with the MOVE being a few pixels late - while offscreen you won't see anything anyway.
Remember, this is not 'somewhat realtime' register manipulation by the CPU like e.g. on the C64 - the Copper runs 'real realtime' and is accurate to four lores pixels. Running pure copper graphics (just background, no bitplanes) you can effectively use a chunky pixel 'high color' display where the color data is interleaved with MOVE commands.
