Depends on the board setup and the admin.
At my board
http://forum.a-10.org/ the troll banning process takes a whole 5 seconds to complete, and there is no discussion required by any of the 4 guys i've given admin status too.
Another board i co-founded
http://www.worldaffairsboard.com/ has a much more democratic process, and there it's a consensus thing. Takes several days to get a troll banned there sometimes.