The elements of the "new game +" work all the time, just after you received them. For example, the achievement for eating canned food gives a bonus - sometimes after eating canned food you will receive additional energy, more than usual. Or, by building a pink rhino club and starting to receive dividends from there, they will grow every time. And if you start the game from earlier savegame, when you get to the club in the story, then the dividends will be big right away and will continue to grow. Same with girls at the Base, unlocked days, etc. All these bonuses are tied to your account, and work in all gamesaves.