No — not any more. The airport’s own FAQ confirms that since 1 January 2022, the free Unireso bus/train ticket it used to hand arriving passengers has been withdrawn. Today you buy a zone-10 Unireso ticket instead: CHF 3.00 (about €2.60), valid 60 minutes on both tpg buses and CFF trains, from machines at the “Genève Aéroport” and “WTC” bus stops or at the CFF station. Hotel, hostel and campsite guests can still get a free Geneva Transport Card from their accommodation, covering the same zone.