No, the pretensioner just has to beat the deceleration of the car. The goal is to retain (or even pull in) the passenger in the seat to reduce the impact on the airbags.

Typically the pretensioner will pull in on the order of 10-12cm of webbing, this is done via a pyrotechnic charge. To be fully effective, the pretensioner would then need to deploy about 110-120 milliseconds before the airbags (which will deploy in 40 ms or so.)

So then it falls on the car's sensors and computer to detect with sufficient advance notice the impending crash. With modern radars (like the ones in newer mercedes cars...) they should be able to gain most of that time at least for frontal crashes.