In my understanding, it doesn't matter how big of a battery you have. It is the load that determines the draw, not the capacity of the battery.
In my case I'm running two matched Optima D31A batteries in parallel. CA 1125 and CCA 900 per battery yielding CA 2250 and CCA 1800 in my setup. No issues (YMMV). I also have a pair of 300AMP slow blow marine fuses, 1 per battery. It is in the dual battery FAQ if you have more interest.
Back to this question. Regardless of how much battery you have sitting in the box, the current going through the wires will be dictated by the draw from the device on the other end as pulled through the fuse blocks and fusible links. If the device calls for more power than the fuses can handle, they pop. It has nothing to do with the size of the battery.
IMHO YMMV I am not a mechanic.