Yes, the travel is fully covered. In certain Bernina Express coaches, should you intend to use this train, a seat reservation is required for the panorama coaches.
Be careful when studying the validity map and check the legend. Dashed lines do indicate the tunnel and have nothing in common with the pass validity. All tunnels are indicated with dashed lines, while a reduction would be indicated by a dotted line.
Hence, you are welcome to use the Vereina tunnel too with your Swiss Travel Pass.