No, you cannot connect the Verbatim PM-14 Monitor directly to a power bank via USB-C and simultaneously to a Nintendo Switch via HDMI to game on the go.

- The monitor can be called via USB-C, but this usually requires that the device it is connected to supports DisplayPort Alt Mode and Power Delivery. A power bank alone is usually not enough to power the monitor.
- Connecting to a Nintendo Switch or other device via HDMI requires a separate power connection for the monitor, as the HDMI port alone does not provide power.

You would therefore need to use a separate power connection for the monitor if you want to connect it to your Nintendo Switch via HDMI.