For an observer standing on the ground with h = 2 meters (6 ft 7 in), the horizon is at a distance of 5 kilometers (3.1 mi).
The Earth curves about 8 inches per mile. As a result, on a flat surface with your eyes 5 feet or so off the ground, the farthest edge that you can see is about 3 miles away
Humans can see from 380–740 nanometers (nm)
So, the answer is no, if you can only barely see 3 miles away, then you wouldn't be able to read the name of a boat 3.1 miles away.
