Impaler Shrike has a triggered ability that triggers when it deals combat damage to a player. It is important to note that this is a trigger condition and not the condition for playing an ability. This means that you choose whether or not to sacrifice the Shrike when this triggered ability resolves. This is the only time you are given this opportunity.

Also, if you do choose to sacrifice the Shrike, then you will draw the three cards at that point. This does not go on the stack as a separate item. If the Shrike leaves play before this trigger resolves, you cannot sacrifice the Shrike and will not be able to draw any cards.