Does Buddhism have a view or agree with the gut feeling? Is this the same as intuition?
In Zen, there's some importance to that. Look at it this way, our mental patterning and habits have a tendency to reign in our perceptions. We fall into traps of our own devising and cut ourselves off from the outside world and even our experience of ourselves. That little bit of stirring, that gut feeling, isn't some mystical voice trying to communicate to you. It's actually your one true voice trying to get in touch from under all the crap you've piled on top of it. It speaks from a place that is beyond thought and knowing in the conventional sense. What it's telling you is usually worth listening to even if it is conventionally wrong. Mind, I said listen to it. Not do what it says. The act of listening is Zen.
See the following:
One Source of Bad Information
by Robert Bly
There's a boy in you about three
years old who hasn't learned a thing for thirty
Thousand years. Sometime it's a girl.
This child had to make up its mind
How to save you from death. He said things like:
"Stay home. Avoid elevators. Eat only elk."
You live with this child, but you don't know it.
You're in the office, yes, but live with this boy
At night. He's uninformed, but he does want
To save your life. And he has. Because of this boy
You survived a lot. He's got six big ideas.
Five don't work. Right now he's repeating them to you.
What is that child telling you? How will it save you in this matter of life and death?