Coming off Optimizely on our headless storefront, does Croct avoid the render-blocking snippet?

our Hydrogen storefront has been running Optimizely and the snippet is a real cost. It loads synchronously on the critical path, and even with no experiment live we measured it adding roughly 400ms to LCP. On a store that lives and dies by mobile that is not free.

I am evaluating Croct as a replacement and the thing I care about is exactly this: does the headless setup actually remove that render-blocking penalty, or am I just swapping one client snippet for another? Numbers or specifics welcome, I have my own LCP traces to compare against.