Answer: It might work, but probably not for the reasons you'd think at first. While I'm always in favor of an experiment, I'm not sure why you would want to do this -- my main concern would be that the soil inside the bag would heat up in the sun and cook the roots before they had a chance to grow deeper into the soil. At first, the extra heat will be a benefit because tomatoes need a warm soil, but later on it could be a problem. If you try it, make sure to mulch well by mid summer to insulate the soil in the bag.
Tomatoes have a big root system, so I suspect the roots will escape the bag and dig into the soil below and that the plastic and soil on top will work as a mulch layer and help keep the lower layer of soil moist. (If the roots don't escape the bag, you will in essence have a containerized plant and will have to water it and fertilize it accordingly.) The hole in the bag will direct any water directly to the root zone, too. To be honest, I think you would be as well off to work some organic matter into your garden soil (say, a bag of compost for each plant), then mulch well and water regularly.
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