Depending on what you mean by "more able to avoid" the answer is yes or no.
The chance of your point defence system hitting the incoming missile is modified by crew grade (I assume this is also true of CWIS but I can't say specifically). So Yes.
The chance of your counter missile interecepting an inbound missile is modified by crew grade. So Yes.
The chance afterwards your ship repairs battle damage is I think affected by crew grade (they should repair faster I think).
Crew Grade doesn't affect how adept they are at following orders, that is what task group training helps. So No.
Your Crew Grade has no effect on the enemy's chance to hit you. Nor does it affect things like Shield Strength or Shield Regen. So No times two.
I don't know about things like ECM or cloaking if Crew Grade affects that.