There is really only one way to determine if that is possible, and that is to recreate a papyrus boat using the paintings in ancient tombs as a guide.
I first read this book many years ago and came back to it recently when copy turned up in the charity shop where I volunteer It holds up very well. Although it is slow to get going, it really gets interesting when they start work on building the boat and is riveting when they are at sea.
There is a point when they are half-way across the Atlantic in the middle of a storm, when you think: "These men are crazy to even attempt sailing a reed boat across the ocean."
The most fascinating aspect of the book is what the journey helps reveal of the sailing and construction details of the ancient Egyptian boats. Details that make no sense on a wall painting suddenly make vital sense after a month at sea. Everything from rope thickness to the way the mast is supported become relevant in the context of sailing a boat that does not have a rigid hull.
Definitely worth reading - if you enjoy this, you'll probably also enjoy 'The Benden Voyage' by Tim Severin, and Heyerdahl's 'Kon Tiki'.