I have simple digital asset in the OBJ level that have nested CHOP network. From CHOP I do a reference in Fetch operator to object that connect to digital asset. Can I export from nested CHOP (it in digital asset) to an object that connected to digital asset?

yes, it's not important where the CHOP network is, the important part is that the fetched data is not dependent on exported data, in other words that you are not creating dependency cycle