Qualify for visa free 72 hr transit if 2 separate itineraries are booked but both are star alliance

I hold a USA passport. Arriving in Beijing from USA Mar 21 on United with a local Beijing hotel stay until departure on Mar 23 on Thai Air to Phuket. These are booked separately thru United. Thailand does not require a visa. I have confirmed seats on all flights and confirmed Beijing hotel reservation. Is this eligible for visa free transit in Beijing?