yes, it will work to eliminate the existing grass. the only problem is tha tevery time you till you bring fressh seeds up close to the surface. i usually till my garden, then a week or two later spray it with roundup, then plant a few days after that. takes care of the majority of the weeds, but you still need to mulch and pull!

google or search gardenweb for "stale bed";

you till up the area & let it sit & get "stale", allowing time for weed seeds to sprout.

Then you till it again!

much cheaper & no more difficult than tilling & then applyng a chemical-
& wouldn't you have to till again anyway?

Or...bury it. Cover the area with cardboard or ten plus layers of newspaper and then 6-10 (or more) inches of any organic material you can find. Leaves, debris from this year's garden, coffee grounds, kitchen scraps, whatever. Maybe sprinkle some soil on it to hold things down, perhaps a spray of water now and then while the hose is out. Let this sit over winter and plant right through it next spring. Or... try a number of methods and see which gives you the best result.

tj

Cover the area with black plastic or old tarp. The heat from the sun will germinate the weed and grass seeds they'll die not being able to grow out of the plastic. ( At least part of them) works for the first couple inches of soil.
Tilling and recovering with plastic will help take care of the deeper seeds. till and recover a couple times the better.