Can the population of the world fit on one continent?

Yes. About 4 or 5 years ago, I read that the world's population could fit into the state of New Jersey. Of course, they only had 2.5 square feet, each.

The issue is in providing food, water, clean air, room to wander about in, sufficient crime control, and so forth. In this sense, the answer to your question is , "No".