No. It’s absolutely ridiculous. It sounds like the sort of thing Westerners who think they understand Buddhism say out of a misguided faith in the supremacy of rationalism.
Consciousness is a physical process that happens in the brain. What we see as conscious brain activity, thought, obviously feeds into itself. Otherwise all thought would be non-sequential, every thought would be a non-sequitur. Your brain would be useless.
Here are a few other claims being made:
Consciousness cannot be measured by physical methods. So, consciousness is not physical. Consciousness is not a physical activity. So, consciousness has no influence on the physical activities of the brain.
The first statement is false. Consciousness can be measured by physical methods, most notably an EEG or other brain wave scan. These scans can determine whether you’re asleep, awake, or dead. Therefore consciousness can be measured by physical instruments.
The second statement has aspects of truth. The contents of consciousness are not physical. When you look at something, we cannot tell through empirical methods what you’re looking at. It’s reasonable to think that we will make inroads on this, but probably will never make consciousness fully legible to science.
The third statement is false. Consciousness is electrical brain activity. If that activity ever stops, you are no longer conscious. If we alter the electrical activity, consciousness is changed. Perhaps they mean consciousness can’t be programmed like a computer?
The last statement is false because the physical activity of the brain influences the further physical activity of the brain, which consciousness will stop if you stop the brain activity.
You see spiritual people trying to assert superiority over science and reason all the time. 99% of the time, they’re just spouting nonsense. Mysticism, real mysticism, and science go hand in hand. Competition between the two is just meaningless theological bullshit.
I meditate and contemplate the divine constantly, I would never try to assert that my findings trump the findings of the scientific community. I might doubt science, science isn’t God after all, but God made science just like He made everything else.
Empirical analysis is just another form of mysticism. Claiming consciousness isn’t fundamentally physical is anti-science and I try to be extremely careful to not be anti-science when I examine it. And most of my insights concerning consciousness come as a result of reading scientific findings.
The soul is non-physical. Consciousness arises in the brain and can be stopped by destroying the brain. The contents of consciousness, mind, is non-physical because you can’t derive them from the physical workings. It is mind that survives death, not consciousness.