Would it circle the globe?
Say 2.5 inches for the pieces, 1.5 for pawns. Each set is 40+24=64 (serendipitously). 64 inches is 5.33 feet. Suppose every person owns one chessboard. There are 7 billion people on the planet. That adds up to 7,070,265 miles. The earth is about 24,000 miles at the equator. But, of course, not everyone owns a chess set. But even if 1% of people own a chess set, that's still 70,703 miles, which is enough to go around the equator nearly three times.
So to answer your second question: yes!
As to your first question: No. Most of them are plastic, and the wood ones are sanded and varnished.
Would you get splinters? Would it circle the globe?