https://en.wikipedia.org/wiki/Reflex_arcSimple answer: No, it does not go to the brain
Detailed answer: We are complex as all hell.
>A reflex arc is a neural pathway that controls a reflex. In vertebrates, most sensory neurons do not pass directly into the brain, but synapse in the spinal cord. This allows for faster reflex actions to occur by activating spinal motor neurons without the delay of routing signals through the brain. The brain will receive the input while the reflex is being carried out and the analysis of the signal takes place after the reflex action.