Of course they are. They are human beings and are as broken as any human being. Like any other human being, they are the result of millions of years of random genetic mutation and natural selection. A process as clumsy as that is bound to create beings with limitations. Beings that fall short of the imaginary ideal of the ideal man or woman. Beings that may be described as “broken”. A scientist is as broken as a non-scientist.
But here is the interesting bit. Scientists know they are broken. They are aware of the limitations that the human condition imposes on them. They understand that it is only too easy to lie to oneself and delude oneself into thinking that they are perfect. They know that it is easy to think of human beings as perfect and infallible.
Scientists know that reality is not all that it seems and that if we allow our senses to fool us, they will do so all the time. Scientists, through the scientific method, learn the harsh truth about reality. They find out the hard way that nature does not give her secrets away to those who are gullible and seek to be spoon-fed by ancient texts. They learn to look through the cracks and tease out an understanding of the universe bit by bit. They calculate and hypothesise and experiment the living daylights out of their brains.
At the end of all this, they are still broken. But they are on their way to being less broken. And that is more than what can be said about those who seek to feel better about their ignorance by calling scientists broken.