In Arkham Horror, do 'leftover' successes after triggering a doom token removal still count?
Yes, left over success rolls do carry over, but the number of success required depend on the GOO that you are facing and the number of players. Also, if the GOO awakens, you always fill up the doom track if it wasn't already full. 

The following is quote from the FAQ which you can find on the FFG Arkham Horror website:


  To defeat the Ancient One, the players must do a total number of
  successes equal to the number of players multiplied by the number of
  doom tokens on the Ancient One. So, if 4 players are facing Yig (doom
  track of 10), they need 40 successes to win. For every 4 successes
  they do, they remove 1 doom token to track their progress. If the 12
  investigators get 9 successes in the first round of combat, they would
  remove 2 doom tokens, and 1 success would carry over to the next round
  of combat.