We can use orphan chunk skipping to make fast count (COUNT_SCAN) accurate in the presence of orphans, similar to what is done for distinct scans, but only in cases where the shard key is part of the index. (To do this more generally, i.e. completely fix SERVER-33753, we would have to push down FETCH into COUNT_SCAN as well, similar to what was done for distinct scans, and for any performance benefits we would want SERVER-94491).

We would expect a performance improvement from this in the presence of many orphans (and therefore a more obvious fix in the actual count), but a small performance hit in the absence of orphans.