Do improvement token bonuses count as skill bonuses when determining the highest bonus to apply to a test?
Improvement tokens are neither a "skill bonus", nor "additional dice", they provide dice in a separate step.


  When an investigator resolves a test, he performs the following steps:
  
  
  Determine Dice Pool: The investigator determines the number of
  dice he will roll. This number is his DICE POOL.
  
  
  •  He starts with a number equal to the skill being tested.
  •  He adds or subtracts the test modifier (the number that follows
  the skill icon on the effect).
  •  If he has an Improvement token for the skill being tested, he
  adds the Improvement token’s modifier.
  •  He may use one effect that provides a bonus (for example “Gain
  +3 Will”). If multiple effects provide a bonus, he uses only the
  highest bonus.
  •  He adds any “additional dice” he gains from effects that apply.
  Additional dice are cumulative and are in addition to other
  effects


Source: Reference Guide, "Tests" (page 11)

Everything, except "skill bonuses" stacks.
Only the effects worded as "gain +X [some skill]" are skill bonuses.
All other effects are not skill bonuses, and stack.