Embora algumas ótimas respostas tenham sido fornecidas aqui, nenhuma delas realmente "fez" para mim em termos de responder conclusivamente à minha pergunta original. Então, decidi procurar uma resposta fora dos domínios do Stack Exchange. Eventualmente, através de uma troca de e-mail privado com um Phd linguista (um não-Trekkie que recusou a opção de se registrar no SE, mas disse que eu era bem-vindo para postar o que ele escreveu) me deu a seguinte resposta:
A metaphor involves using language for non-literal meanings. This presupposes that literal meanings exist and are known, so a purely metaphorical language could not exist. If everyone only used metaphors, then these would become the literal meanings (this can be seen from examples of changes in meaning to words such as 'toilet' - originally a bag for clothes, the meaning shifted to the act of getting dressed, which again shifted to a metaphorical euphemism for the room you shit in; with such frequent use to refer to the room this is now the literal meaning). All language use is based on the social acceptance of arbitrary pairings of sequences of sounds (or symbols) with objects/activities etc. In many cases, one particular pairing is taken as the default or literal pairing and then any uses of the word to refer to other things is taken as metaphorical. An example of this I was thinking of investigating a few months ago is similar to that for 'toilet'. Metaphors are generally used in 2 different ways: poetic (All the world's a stage and all the men and women merely players etc.) and everyday (for example, one metaphorical grouping for the idea of happiness is 'up' e.g. I'm feeling up; That boosted my spirits; My spirits rose; I'm in high spirits; That gives me a lift). The everyday metaphors are so pervasive that we don't think of them as metaphors any more (at least if we're not being facetious). This has sparked a whole new area of linguistics where researchers analyse everyday metaphors to gain insights into underlying thinking and is most often used to analyse political discourse. I attended a talk where the metaphors of Nigerian politicians were analysed leading to the conceptual view of the politician as a builder (based on 'build the economy' 'the foundations of the nation' etc.). All of this seemed to be reading too much into language use so I started looking into the etymologies of some of the words analysed. 'Foundation' for instance was used for founding an organisation before it was used for houses, so the building use is actually the metaphorical one historically. Anyway, what I'm trying to say here is that any frequent use of a metaphor becomes literal, and with only so many comprehensible ways of making metaphors for a given concept, the metaphors would have to be repeated and so not be metaphorical any more. So, my first argument would be that the episode is based on an invalid assumption - communication entirely by metaphor is impossible.
On a more technical level, it's unclear whether the language should be considered as using metaphors. There's only one example on the Wikipedia page, but this seems to concern the distinction between the locutionary and illocutionary force of statements, rather than metaphors. If someone comes into your room and says 'It's hot in here', the locutionary force (or literal meaning) is a statement about the temperature. However, you will be thinking about why the person said that and (depending on the circumstances) might interpret it as 'Can you turn on the air conditioning?' - the real intent behind the statement or its illocutionary force. "Temba, his arms wide" is interpreted as having the illocutionary force of 'You are willing to share'. The problem I have here is how the universal translator would work to translate the statement as 'his arms wide'. If there is no dictionary available which gives literal meanings, the translation system would have to work on matching phrases (at least initially not divided into words) with what happens in the context in which the phrase is used through probability. If 'his-arms-wide' (pronounced 'ekifantup' or whatever) is often used in contexts where sharing follows, then the translator would translate 'ekifantup' as meaning 'you are willing to share', not as 'his arms wide'. This has implications for your actual question - how would children learn? There is increasing evidence that children act as probability analysers in interpreting the input they receive (it's only when adults analyse language that we look for rules), so with enough exposure a kid would behave like the universal translator should and take 'ekifantup' as meaning 'You are willing to share'. The metaphorical meaning will have become the literal meaning, and the previous literal meaning will have disappeared (as 'toilet' meaning 'getting dressed' has except in old novels). So you are right in saying that children couldn't learn a purely metaphorical language, but the reason is because it wouldn't be a metaphorical language any more.