From the YT clip I would not be surprised if this was recorded somewhere that wasn't the Ed. And the graphics could certainly have been planned with an October 17 airdate in mind. Not sure if that would have had an impact on how the vocal appeared in sync (or not) with the audio. Some of the YT comments think she may have been singing to a track with vocals, but there's no consensus (surprise!). For a Late Show music segment, it's got a lot of views (171K in the 24 hours since release).
NPR Music released a Tiny Desk Concert by Ms. Polachek last week.
This concert makes me think Polachek has serious vocal control, and can use her voice to produce tones that resemble audio that's been modulated or otherwise processed (think of this as a variation on singers who can produce overtones like in throat singing). The video description notes that Polachek has been criticized for sounding like she uses pitch correction software, but the NPR performance didn't use that or any other vocal processing.
None of this means that the Late Show performance wasn't lip synced, but it makes me think that some of what sounded artificial in that performance may indeed be natural to Polachek.
David