If a PhD student is bad in interpersonal communications, would he find trouble doing his PhD?

Of course interpersonal skills are important in completing a PhD. As you note, a PhD some fields involves working in small to very large teams, where interpersonal skills are essential. Even in the few fields were individuals typically work alone, interpersonal skills are necessary to navigate relationships with peers, graduate advisors, other members of the community, etc.

This is not to say that with poor interpersonal skills one is doomed. Such skills can be learned, and one can improve substantially with effort. It may even be true that in some areas of science, interpersonal skills are less important than in other jobs. But to say that they are not needed would be a gross misrepresentation of what it is like to get a PhD or work in academic science at any level.

Suppose, a PhD student is either introvert or bad in interpersonal communications or both.

Would he find any trouble?

All of us, in academia and outside of it, are better at some things and less good at other things. People who are very poor at interpersonal relationships are often astonishingly good at many things. To be successful, one tries to exploit one's talents while at the same time overcoming or learning to work around one's deficiencies, or even turning one's worst liabilities into assets in some surprising way (e.g., a comedian making a career out of making fun of themselves for being a neurotic slob with bad habits). Some people have even become famous for completely overcoming a significant adversity in the form of a physical or mental disability that stood in their way of becoming successful at something. The case of Oscar Pistorius is one example from sports that comes to mind (notwithstanding his later downfall into infamy by being convicted of the murder of his girlfriend), and there are many other examples.

In the context of academia, unquestionably the most famous person who can be cited as an example in connection with your question is Temple Grandin. I saw her speak a few years ago when she came to my university, and she is a remarkable and awe-inspiring woman. I couldn't begin to give a good description of how amazing she is, so I recommend checking out her books, or watching the movie (starring Claire Danes) made about her. Suffice it to say that she grew up with autism, and having a fairly extreme case of being "either introvert or bad in interpersonal communications or both", and yet became a stunningly successful animal scientist (her main job is as a professor at Colorado State University). She is a great inspiration to many people who are either on the autism spectrum or are just extremely introverted or different from what is thought to be "normal" in some other way, and part of her advocacy is in convincing such people and their families that they are often capable of achieving a lot more than the society around them assumes.

Bottom line: if Temple Grandin could succeed, so can the PhD student you are asking about. And besides, many other less famous people in academia are both introverted and not especially good at interpersonal communications, and become very successful anyway. I'm not saying it's necessarily a good thing to be, and it may make sense for your friend to work on getting better at those things, but I absolutely wouldn't assume that it will be a career-killing problem.

The answer is simple: Yes, someone who is heavily introverted, has bad interpersonal skills or both will have trouble doing his PhD. Someone who has these social issues will have trouble doing anything in life. Even the simple act of existing in modern society requires at least some modicum of interpersonal skills.

This doesn't mean it's impossible at all! In fact, although I have no data to support my claim, I would estimate that the chances come out about equal for such a student to complete their PhD compared to the average student. It will simply require more effort from them. Every student has their weak points and strong points, most weak points can be strengthened and some can be partially or even entirely covered for with their strengths. The most important thing is to have the will to succeed.