Could probably be realized using Tasker:
- Condition: Boot completed (or Monitor Start)
- Task: Start App
Not sure if you can specify a video file directly here. But there might at least be some video player supporting to automatically start playing the latest playlist, which should make up for it.
You can find a free 7-day-trial of tasker on their homepage -- or try alternative automation apps such as e.g. Llama - Location Profiles. Another possibility is to create the profile with Tasker, and then export it using the Tasker App Factory; this way you'ld get a "free version app" of your profile to distribute on the tablets.