There are a lot of people who do it, so its clearly possible. But, as with anything, the larger question is whether its possible to make a living at it and still maintain your passion for it and still love it? This is much much harder and much rarer out in the world. I know a number of wedding photographers who make a living but don't really enjoy it much - its just a job now... There are probably some photo-journalists who still love it. But I don't think there are many street or landscape photographers out there making a living and loving it. Maybe a few from the big magazines, but its pretty rare.
Then again, the question reminds me of the old joke, "If you want to end up with a million dollars as a photographer, start with two million"! This is often applied to bike shops, jazz clubs, other jobs that people go into with a lot of passion and come out of exhausted and broke...
I grew up looking at the pictures in my father's National Geographic magazines before I could even read. David Attenborough's documentaries were also a staple in my childhood. I can only dream of getting into this line of work as a career. It would be beyond anything I can imagine to be a NG photographer on assignment. It's part of why I quit my career job to go to film school and study documentary filmmaking. I would certainly immerse myself in the stories I am assigned to and get that story, or get that photo.
About five years ago when I changed careers I looked at doing a photography course, but it occurred to me that there would be very few photographers who are good enough to spend their lives documenting events and locations around the world. For most it would be staged shots of children in shopping malls, school photos, uni graduations, weddings...fine if you like that sort of work but I don't think I would have ever picked up a camera for fun again.
I agree with this also. Start with a secure source of income while you build your own business on the side. Be you must be prepared for lack of sleep, it depends on how committed you are to make this work.