That's "possible" in the same way that wizards and vampires are possible - sure, I can't prove it's fake, but there's not a shred of evidence, plus it would upset everything we've learned about the universe.
Cells, tissues, and organs undertake a variety of self-maintenance behaviors without the direction of the brain. Although low-level behaviors like these are abundant, high-level examples also exist, like when an arm pulls away from a hot stove as soon as the signal reaches the spinal cord. The organism is a recursive system, with sub-systems behaving with varying degrees of autonomy while also depending on the larger system. The seat of consciousness possesses only a limited view.
Neurons do not have a brain. They do not have emotions or feelings or thoughts. This conversation is so absurd that it's well into the realm of fantasy.
What causes a neuron to perform its functions if it isn't some brain? The answer would likely be physics, and I would say that first-person experience is fundamental in the physics if it exists at all.
Or somekind of electrical system, acting as a software layer on top of the hardware (neurons) layer. This electrical thing is what controls and orchestrates everything and also is our ego.