not really,if that was really the case,then it will be more eradicated that just what we see in the game(and again,if that really is the case,then with only one sonic could have saved little planet,but not,in the bad ending,if he does not get them all,he will not save the planet)
in the manuals it sounds more that sonic can keep the speed to make the time travel,and that the time post are things that allows him to know where he needs to go,and one developer(naoto oshima)says that the idea of the game was that sonic goes fast and the levels change.
here is the interview.