Well certainly you can see a difference in soil for a while where woodland has been, after it's been chopped down. And different soils obviously support different vegetation. But his view sounds rather imaginative. Or looking at things from the wrong direction (with the causality going the other way). If you want to keep a view you can always cut down the vegetation with your axe. But any inference you can make about prehistoric vegetation what with all the intervening years / interference.. The only places you can do that are boggy places where the local pollen's been preserved, I would have thought.