I feel that many words if not all of them have a direct mapping to some kind of inner subjective experience, to a physical object, mental feeling, process or some other kind of abstract thing. Given that machines don't have qualia and no mapping of this kind, can they really understand anything even though they are made to answer to questions with lots of statistical training?
I'm going to be controversial here; so please don't vote this answer down if you just disagree with it.
Your question presupposes that machines do not or cannot possess qualia, which are required for true understanding. Given that we don't really know what it means to 'understand' something, and that even the meaning of 'meaning' itself is by no means a resolved issue, it might be overly specific.
In one strand of linguistics, the meaning of a word is defined by its use, and by the context of surrounding words. We could hazard a guess that children acquire the meaning of words through exposure to language, and the correlation of experiences with the corresponding sounds. How that works in detail is AFAIK not fully understood. But there would be nothing 'inherent' in a new-born human that would enable it to 'understand' anything.
If that is the case, then we could train a machine to do the same. Obviously, it would be a long and tedious process, and there is probably a reason why it takes us years to become proficient in our use of language. But if we correlate sensory input with linguistic utterances, a sufficiently sophisticated learning algorithm might be able to acquire some meaning for such utterances from the way they are used.
There are, of course, rather a lot of unknowns here. That is because the topic straddles various fields, from child language acquisition, corpus linguistics, the psychology of learning, and many more. And to my knowledge, none of these fields is sufficiently advanced to shed any light on this issue yet. There is the whole question of abstract words and concepts. How do we segment the continuous stream of sounds into discrete units (phonemes) without knowing what they are? With all that complexity I begin to appreciate why Chomsky opted for his Language Acquisition Device to avoid getting frustrated... :)
So, to answer your question: yes, it should be possible. A properly set up machine, which would be able to simulate human learning, would pick up its own mapping of linguistic structures to its experience from the world outside. And if we call this mapping the 'meaning' of those structures, then a machine can learn this, and presumably 'understand' language. If we ever get to that stage with AI is another question.
We don't even know exactly what qualia are, so it's hard to say for sure. But here's what I do think: a lot of human learning is experiential and is rooted in our interactions with the physical world. That is, we see,smell, hear, and feel things, we experience gravity and our orientation in the world through kinesthetic awareness, the sense of balance we have, etc. So while an AI running on a server in a data center might well be "as intelligent" as a human, I don't think it's reasonable to expect it to have the same kind of knowledge and awareness as a human, simply because it has never experienced many things.
So if you want to talk about, say, "seeing the color red" and refer to qualia, then sure. I think it makes a certain kind of sense to say that the machine will be missing something "human" and that that refers to qualia.
OTOH, I think it would be a mistake to underestimate just how "intelligent" our AI's will eventually become even if they aren't embodied. We just have to keep in mind that their intelligence might not be quite the same as ours, because they essentially inhabit a different world.
I think a "successful" strong AI with natural language abilities -- say one that could produce "good" unsupervised translations of literature, or pass a rigorous Turing test -- would have to include in the corpus of data used to build its models visual, auditory, and probably tactile data. It might be necessary as well to simulate the kind of agency and intentionality that humans have-- so the AI-in-training has the opportunity to move a simulated self to change what input it receives. I suspect training it only on text data, for example, would always be inadequate. If it had access to sensory information and learned to associate it appropriately with the symbols of language, it might be able to learn the meaning of language in a way that we'd find difficult to distinguish from our own understanding, even though the AI would presumably not have the (same) qualia we have.
Of course, we are a long way from having hardware sufficiently powerful to even attempt such a comprehensive mind-modeling project. But I don't think the qualia issue in principle prevents a "real" understanding of language; its just a matter of extending the symbols available to the AI for modeling the world represented by language to be a good enough match for the symbols humans use in their minds, including the symbols that arise from sensory inputs.
Great question equally qualified answers. My belief is yes to understanding language and the bugaboo (a non intellectual vernacular) is what is understanding. Is it interpretive? Inferred? To what end? An algorithm's response to a command in language form will depend on the robustness programmed into it. However, qualia connotes a subjective experience due to a sensory stimuli whether triggered by memory or one of our human senses. Then it begs the question of can a computer collectively experience and how would we know that. Second, are all algorithms subjected due the the programmed bias and it's available data store? Facebook and Google news have shown that programmed bias is very real. Furthermore, Qualia is an emergent trait so I can't see how a computer and it's collective systems can become aware and have subjective experience.