as long as the snakes hunt them, yes. other predators of the funnel spiders include birds, small mammals and reptiles but the article wasn't very specific.
and just what you wanted to hear "Centipedes are expert funnel-web predators, and will readily enter the retreat, attack and consume the occupant"
centipedes give me the hibby jeebby's though...
is there a grey spot/area on the top part of the abdomen? just to make sure it isn't a mouse spider, hard to tell from pic.