Not at all? Well, it is possible my translator (leo) is wrong. I think i have a fairly good understanding of the english language, but i am not a native speaker, so i tried to check my understanding.
I still think it has in this case at least the connotation.
That is the link: http://dict.leo.org/ende/index_en.html#/search=barely&se...
Anyway, if I were learning English I'd pay the $300 for an Oxford English Dictionary. You'll learn a lot that way.
This is a special case. I know that normally barely meanst "only just" (though i believed leo that it sometimes - in special cases when used in a specific way - can mean "only almost"). But if someone hears a sentence like "that is barely visible", one always implies that it is not visible at all for someone seeing a degree worse. Now, if you vist a pornsite with usergenerated content - take 4chan as example - I'd bet a lot of money that one would find a mod-guideline or at least a discussion about such a guideline to delete any threads with "barely legal teens" as topic because a lot of users would post pictures of underage girls in such a thread. In such a case, barely implies not really. And therefore such a term can have another connotation than its formal meaning.
It is really a stretch to say "it doesn't have that connotation", connotations can vary even in one language for every speaker.