Can I use the 7" HDMI monitor without access to the power button?

I would like to use the 7" HDMI monitor (sku 104990443) as a secondary screen in a custom pinball cabinet, attached to a Windows 10 PC. But the screen would be mounted internally within the cabinet so I would have no access to the buttons on the side or the HDMI cable. What I need to know is whether the screen will turn on automatically when power is supplied and work in this configuration.

When the PC is turned on, a “smart power strip” will also turn on for the monitor’s power supply. Will the screen turn on automatically when powered, and will it be able to negotiate the HDMI connection regardless of power-up order (if the PC comes online first or if the monitor turns on first)?