Should a curtain drain be covered/back filled?
The usual purpose of a curtain drain is to divert (under)groundwater away from a structure. The only reason to not cover it with fabric and a few inches of soil is to capture surface drainage as well. If you need to capture surface drainage, then there must be a significant grading issue that is allowing surface water to stand near the structure.

Such a grading issue should be corrected, in which case the curtain drain could be covered. If for some reason it cannot be corrected, (or this is actually a gravel filled trench drain) then the gravel should be left exposed. It will also need to be maintained so that it does not get clogged with silt and other material carried in surface runoff.

In summary, the proper surface treatment depends on the intended purpose(s) of the drain.