No, that doesn't help at all. Leaving tap water out for a day is exactly as effective as leaving it out for ten minutes - which is to say that the only thing it gets rid of is chlorine. Chlorine isn't a huge problem for carnivorous plants, though, so it doesn't get you anywhere. On the other hand, a little bit of water evaporates off when you leave it out, which actually raises the concentration of dissolved solids in the water. So really, if leaving it out makes any difference at all, it's making the water worse.
You MUST use rainwater (collected from a clean surface, not out of a stream or puddle or something) or water filtered through distillation or reverse osmosis. Everybody tries to cut corners here when they're starting out, and it doesn't work in the long run. A gallon of reverse osmosis or filtered water costs like 40¢ at the grocery store; a home reverse osmosis filter costs about $100. Finding a way to skip filtered water really just isn't worth the savings.
There are people who succeed without filtered water, but most of them learned to do so through lots of trial and error, and the rest were probably just lucky to live in a place with really soft tap water. Until you've learned enough about soil chemistry and botany to understand the scientific reasons behind why hard water is harmful to CPs, I would suggest ignoring anyone who says that you should use tap water, brand-name bottled water, etc. And anyone who tells you to use boiled water is badly misinformed - there's simply no reason why boiling would help.
~Joe
PS - Note that, while chlorine evaporates quickly from water and is relatively harmless to houseplants, some municipal water supplies use chloramine, a chlorine-based chemical which doesn't evaporate. I don't know if it's hazardous to CPs in particular, but I know many houseplants dislike it. I think there's some common household substance that can be used to break it down, but I don't remember what.