Do you want rain and sunlight ot make it grow or do you want to kill off the weeds? There are much better ways to do this but they do require some work but are much better for you and your garden in the long haul.

Yes, you'll kill off lot's of stuff under the plastic. You'll still have to pull up some of the stubborn weeds that have turned albino under the dark cover. The longer you can leave it down (more then a year?) the better. Then heavily amend the soil with compost before you plant.

Word of caution: The plastic doesn't let any water through, so if your killing off weeds, say under a tree or some shrubbery, you may be doing drought damage to those plants as well.

Cheers.