According to the biologists, no. There are no cusk (burbot) in that watershed.
You'll need to head west and try Seymour, Echo, Willoughby, or Memphramagog for cusk.
BTW, the Connecticut River watershed does have cusk. Even the small streams just east of the Averills have them. Weird, huh?
There should be plenty of small, hungry lake trout in Little Averill to keep you busy, though. Remember, that lake only allows 4 lines and has a 1 fish limit (21" minimum).