Some other cases exist in which you are not delayed. For instance, if you enter a gate willingly as result of an encounter. There is one at the Newspaper where Doyle Jeffries asks you for an avidence of the Mythos, and you gain a Retainer card if you enter a gate. In this case, I'd say you're not delayed as well.
In the OP's case, I'd say the investigator is not delayed as well (the encounter has an effect similar to a failed combat check against a Night-gaunt; if the Night-gaunt does not delay you, neither this encounter should)
(and of course, in the last few months I've played so rarely AH, that I can't imagine Tibs or someone else nailing me down for this answer ::laughter: