In Arkham Horror, if a monster surge exceeds the max allowable monsters, does the monster that caused the max to be exceeded get discarded?
Yes. See this example from the official Arkham FAQ, p.12 (emphasis mine):


  In a 3-player game, the  monster limit is 6  and  the  maximum number
  of monsters in the Outskirts is  5. There are 3 open gates on the
  board, 6 monsters in  Arkham, and 4 monsters in the Outskirts. During
  the  Mythos Phase, you draw a location that already has  an open gate,
  so you have to draw 3 more monsters.  You would first draw 2 monsters
  and place them in the  Outskirts. The Outskirts limit would be 
  exceeded  upon  placing the second monster, so you would then increase
  the terror level by 1 and return the six monsters in the  Outskirts to
  the cup. Finally, you would draw the third  monster and place it in
  the Outskirts.