If you travel back by changing the game's time then the villager's house would be there. I've heard that if you change the 3DS time instead then the opposite would happen, so the plot would disappear
No. Unless my own experiences were different or something's changed with the Welcome Amiibo update, once you've loaded your town and there's a plot down, that plot's there to stay. Time travelling backwards any number of days counts as going forward one day, so in your case, going back to the 4th wouldn't make the plot disappear. It'd simply put that new villager IN their house, ready to move in.