Is it essential to run the reactor effluent to protein skimmer?*

Ideally yes. Without the physical removal of the bacterial mulm, there is no pathway to remove fixed nitrate and phosphate from the aquarium. This will usually entail putting the reactor in line between the protein skimmer feed pump and protein skimmer itself. In cases where the protein skimmer feed pump exceeds the required flow rate through the reactor, it can be plumbed in via a bypass line which can be adjusted via an inline tap.
_(See Image below)_. In cases where a sump based protein skimmer is used, the reactor should be run from its own feed pump with the outlet directed towards the protein skimmer intake.