Speed of query depending on document size

Working with Data
1

Does query`s speed depends on document size?

For example I have aggregation with $lookup, $unwind and some other steps. If I add step $project, which project only required fields for me after $unwind, does this action speed up query?
Or it does not depends, and MongoDB works with documents with 5 field and with documents with 100 fields with same speed?

2

In one particular case, I am pretty sure it makes a difference. If the 5 fields are part of a compound index and the project is near the first match, then you avoid a FETCH, which will bring the whole document from storage to RAM, which is slow.