Sure.
Sometimes there really isn't the exact word for a given description. There have been thousands of years of language work, in stories and technology, where people have created the refined vocabulary of the world's languages. But just as the Cro-magnon (probably) didn't have words for 'vacation' or 'stirrup' (certainly they could understand and describe those concepts), we (all the world's languages) have quite a few similarly complicated concepts for which we have no single word.
However, as a student of a foreign language or someone rising through an academic career, one is getting acclimated to the more rarefied areas of concepts, where most people don't go often, but those who go there need to save space and time and thought by using abbreviations of descriptions that collapse into single words. Then there is the tendency to believe that there will always be a single word for a complex description, because every time they look beyond the horizon of what they know already, there is a new word for a new concept.
This is all to support your assumption that there truly are situations where there is no single word for a description.
Now to your point, 3) should we 2) encourage 1) giving 'no such word exists' as an answer?
We've justified that sometimes that 'no such word exists' is the case. But that is only sometimes. Other times it is a matter of tip-of-the-tongue or memory or lack of experience or rarity or obsolescence or lexical gaps (no one 'designs' a language systematically from scratch and so some slots just happen not to be filled, sometimes even when there is a need).
This meta question is encouragement enough. Asking the leading question "What is the single word for ...?" implies that there must be one, when there isn't. Suggesting in comments or editing the question to "Is there...?" is enough.
What you should always do is answer knowledgeably. A bald answer like "No, there is none." is a terrible answer. A positive answer of a single word is also terrible but there is some hope in being able to look it up in a dictionary. With "no", you have to explain that absence of word is, in this case, by much experience (which is not very justifiable by authority), evidence of the true lack of the word. (A systematic proof of the lack would have to be a laborious comprehensive listing of 'all' words and for each one justifying that they don't match the concept.)
So in the end, sure, for a single word, if you can justify with some knowledge that there is no such word (hopefully with a good thesaurus that gives the small neighborhood of related concepts where you can say "in this neighborhood there is no such word that matches exactly what is sought"), then yes, answer that way.
Even though such an answer may be correct, it will most likely not be a high scorer; no one like a negative answer even if correct.
