According to the link in @RaizinM's comment, 'vico' can mean either "turn" as in turn in line, or the line itself. I would argue that if there is a line or queue that someone can possess, this would be a valid sentence. Like you said, someone could say something about their coworker's checkout line/queue by saying "via vico".
His flat accent on my computer (without head set), makes the Esperanto hard to hear at times. Ni, Vi, Mi sometimes get lost in transmission via my expensive laptop but somewhat less than good speakers! You may hear the syllables clearly, but others do not, and I have read a number of reports on the Duolingo Learners Facebook page; that others have trouble with the low flat accented audio of this course. The "liaison" not like French in this phrase, but when you listen to this phrase, it sounds like he uses liaison between "via" and "vico"!!
Esperanto doesn't have letters that are only pronounced in the case where otherwise two vowels would follow each other. But I also can't hear what other sound you hear between those two words, regardless of how far I turn up or down the volume. If the sound is still the same as it was then, then I've no idea what you're hearing.