Not according to the weight of evidence...

Lower Shipping Requirements
Since plastic bags are normally much thinner and lighter than comparable paper bags, it would take at least seven 45-foot trucks of paper bags to deliver the quantity of bags contained in one 45-foot truckload of plastic bags. Consequently, the use of plastic bags reduces road traffic, the resulting air pollution, and truck fuel consumption.

More Natural Resource Consumption?
Polyethylene is derived from comparatively small quantities of natural gas. All plastics and chemicals use less than 10% of the total oil and gas produced in this country (most goes into transportation and heating). In contrast, paper is made by destroying trees. Both have an impact on diminishing resources and although fossil fuels are non-renewable future plastics may be made from renewable sources (in the way that we now have managed tree plantations for paper)

Pollution, Environmentally Safe Products:
Plastic bags are an environmentally safe product to produce. The majority of kraft paper is made by heating wood chips under pressure at high temperatures in a chemical solution and paper production generates more air
and water pollutants than plastic bags.
Paper is made by pulping wood and other materials in water. The wet material then has to have the water removed. This is done by heat and pressure. The fossil fuel required to drive the water out of one paper bag is more than the amount required to make one plastic bag.

Recycling
It takes less energy to recycle a pound of plastic than it takes to recycle a pound of paper.