Suicide attempt

A 60 year old man attempts suicide by taking a drug overdose. He is unconscious, but is starting to improve and may regain consciousness within a few weeks. However, he was not breathing for a short while after the overdose and likely sustained some brain damage, though how much cannot be said until he regains consciousness. He has left no Advance Directive. His family requests that he be taken off of life support and allowed to die. Is it OK for the care team to honor that request?