Is there some truth in modern American accents being closer to the original English accents of 17th century?

It depends on what you consider an "American" accent. In the New York/New Jersey area where I live we speak with totally different colloquialisms than those in say Alabama, who are again different from people who live in Minnesota, who are also different from people in California. There really is no one singular "American" accent, so it's almost impossible to pin down what it would sound like compared to the old English accents from the 1600s.