You are correct - you can disconnect the tether from the topside device to power off the ROV. Do mind however, that once the tether is connected to the topside device and the ROV is powered on, it takes anywhere from 1-3 minutes for both the Raspberry Pi (on the Trident) and the Topside WiFi device to be fully booted up and connected to.
We don't have an exact calculation of how long the ROV will remain on when powering the Raspberry Pi + WiFi. Your use case could possibly work, but we don't know. @Walt_Holm what do you think? He wants to leave the ROV on for up to 12 hrs and use it semi-actively for 3-4 hrs / day.