No. The airport’s own site is explicit: “Passengers require a special ticket for 100E Airport Express.” It costs 2,500 HUF (2,200 HUF before 1 October 2025), buyable on board by bankcard through Budapest Pay&GO or with the BudapestGO app, and it is valid for a single one-way trip on that line only — it does not let you transfer to or ride other lines.