I think it is not a good idea to process the cocker Naptha directly in the hydrotreating reactor bypassing the diolefins reactor. Because high olefin content will result in higher catalyst deactivation, higher hydrogen consumption, and a higher temperature rise across the catalyst bed. Further, silicon and high sulfur content will also cause catalyst poisoning and higher deactivation rates. The hydrotreating HDS/HDN reactor needs to run under severe operating conditions to meet product specifications.
The Fractionator column will have less flow of lighter naphtha range, but I think it will not be so much problematic. If the naphtha flow is too low, that fractionar can’t run properly, then the minimum flow of coker naphtha can be processed. Otherwise, it is better to not process the cooker naphtha without passing through the Diolefins reactor.