Can I use cast iron on a hot plate?
You can use any kind of pot on a hot plate. I can't see any reason cast iron would be a problem, unless the hot plate has a less durable surface and you're worried about scratching it.

The only thing that matters is whether the hot plate is powerful enough to keep your food above 140F for the entire time period. That depends much more on the size of the pots than the material they're made of.

If possible, I'd suggest checking with a thermometer to confirm. You can always do a dry run, and you don't have to wait 3 days. If it holds steady at a safe temperature for an hour or two, it should be fine.