Can't say about an oversized rope, but be careful about hanging it with an oversized sling. At Parks, we have a larger ISC, which is sweet. My supervisor previously has successfully used it with a lifting type yellow eye and eye sling, or green cordura covered endless loop sling. whichever one it was, the sling was oversized and the force was pushing out on the side plate where the lateral restraint is only a small pin.
Sherrill had a warning and illustration about this same point in a recent catalog.
No harm done to the block that we could see, and no mishap, but a hard pull with the block as a redirect, which we often do in semi-critical situations, would not be a good time for a failure.
I haven't heard of this happening, but a screwed-in anchor pin has its value, IMO.
The lightweight of the ISC is Sweet.