Nyogtha sends his tendril any time a monster occurs during an encounter. Presumably this would apply to OW encounters as well ---- if the tendril is already somewhere in Arkham, then it seems to me that the tendril is sent to the OW encounter, & regardless of the outcome returns to Nyogtha's sheet afterwards. Am I correct?

Basically. The Tendril appears whenever you have an "A monster appears!" encounter, but monsters that appear as a result of such encounters never remain on the board afterwards. Thus, the Tendril will always return to Nyogtha's sheet and be available for the next such encounter.