your right in that they can not shrug off the insignificant characteristic itself but they can shrug off the effect which gives it to them.
if Hamlin casts understand the soulless, at sue. sue would be insignificant. sue then decides to shrug off the effects of understand the soulless. he is no longer insignificant. with excessive bleeding an effect is put on the model which makes them insignificant and make a wp duel or die later. also can be shrugged off. since all of the above sits on the model.
Can you clarify what an effect is?
An effect meets all of the following criteria:
It is generated during an Encounter
It sits 'on' a model
Paralyzed sits on the model which is Paralyzed
.
Conduit sits on the Voodoo Doll.
Nurse's Massive Dose sits on the target of the Spell.
Has a defined end time
Excessive Bleeding lasts until the end of the Encounter.
Wild Heart lasts until the end of the Turn.
Damage Effects end once the damage has been applied
and you have started Damage Resolution.
What is not considered an effect?
The following are not effects:
Models
Anything printed on a model
(although they may generate effects)
Terrain
Markers/Counters/Tokens Wounds
A Model’s State
(Model states include: Falling Back, Killed, Sacrificed, Buried
all pulled strait from the faq (heh excessive bleeding is right in the faq)
so to answer OP yes it can be shrugged off. (albeit comes with withdrawal lol)