Is there brain function during a cardiac arrest?

No. Cardiac arrest means- heart not beating, hence no blood flow/ circulation- brain does not function when there is no blood supply.
For a brief time. When the heart stops circulating blood to the brain the functions of brain cease after about 5 minutes. If CPR is performed the brain function can return. However prolonged CPR may not get enough blood to brain to prevent brain damage even if heart recovers.

Related Questions

Can your brain still function after having cardiac arrest?

Yes. Depends how long the brain was without oxygen - if the patient was immediately resuscitated, many of them recover completely. Read more...
It depends. It really boils down to how long the brain was deprived of adequate blood flow. This depends on how long till the heart started functioning again and how quickly good CPR was started. The longer the brain goes without oxygen the more chance of brain injury. Read more...