Probable, but not an absolute guarantee. The first Group IIIs refined in Europe were made from solvent dewaxed Group Is without the aid of hydrocracking. They had the requisite VI of 120 and up, but still carried the higher levels of sulfur (>3%) and aromatics (>10%) typical of Group Is. Hydrocracked Group IIIs contain less than 3% sulfur and less than 10% aromatics. When gas-to-liquid (GTL) Group IIIs (absolute iso-paraffins) generated from "stranded"* natural gas become avaialble in a couple more years, they'll have near zero sulfur*, no aromatic* content and a VI of 140 or higher.
*"stranded" refers to the natural gas that's traditionally been flared at the well-head or refinery because it's uneconomical to collect and distribute where needed. Now, there'll be a use for those nearly pure hydrocarbons. Natural gas is 90-95% methane (CH4) with almost no sulfur content.