It is not clear the context in which you expect an answer. For example, should it be considered from a legal, ethical, survival, or psychological standpoint? I would expect the answers aimed at different philosophies to differ quite a bit. Let me address a few of your questions, at least as I understood them in your posting.
Can the person being "ignored" feel impotent as a result of this "silent treatment"? Of course this can happen. However, this reaction is not something that should be blamed on the person doing the ignoring. After all, if you look at someone funny and they throw a tantrum, is it your fault they cannot control themselves?
"Can emotional detachment be considered as a dysfunctional behavior for the victim of a verbal aggression?" Dysfunctional is not a term that can be legitimately applied here without context. There are many cases where ignoring a verbally abusive person can be extremely useful or even necessary to carry on with daily activities. For example, if people talking on forums got caught up responding to trolls, they would not be able to have reasonable discussions with non-trolls. A troll is a perfect example of a verbally abusive person for which silent treatment is clearly not "dysfunctional". The key thing you have to understand here is the intent of the verbal abuse. If the abuser is simply trying to reason or convey a message, with no hidden agenda, then reasoning in response may be fine. However, if the verbal abuser is socially sadistic, such as a troll, then the worst thing you can do is to get emotional in response to his or her provocation. After all, that would be accepting the damage they are trying to inflict for their sadistic pleasure.
Should a person "demand empathy" instead of ignoring the abuser? Successfully demanding and receiving empathy requires two things: (1) You must be deserving of empathy, which is highly subjective, and (2) the abuser must be able to feel empathy. The former requirement could necessitate skills in persuasion, which not everyone has. Furthermore, if you are being verbally abused because you legitimately did something wrong, you would need to show that you understand your wrongdoing and truly intend to make things right. The latter requirement depends on the personality and mental state of the abuser. A psychopath, for example, would not be able to feel empathy, so there would be essentially no point in trying to demand empathy from them. In fact, it would be dysfunctional to demand empathy from a psychopath. Such would be like demanding a shower head to dry you.
"[Can] emotional detachment can be considered hostile / aggressive?" Hostile perhaps, but I cannot see it being "aggressive" since it is in the very definition of the word that force be involved, which clearly is not the case in reactionary abstinence. Sure, there is such as thing as "passive aggressive", but the term itself is practically oxymoron. A more correct term would be "passive hostility".