leave rear hatch open for long time?

For a few hours, no. You can turn off the little light on the left, which will reduce the power drain. You could also leave the car in ready mode, so that the engine starts up as needed to recharge the battery. The mileage will be lousy, obviously, but at least you won't be stuck.

 

Once the trunk light is off, why would the car care that the trunk is open?

 

I regularly leave the hatch open for extended periods of time, including camping and have no problems as long as the little hatch light is switched off.

 

Yes, even if the cabin lights are turned off. This is because the body ECU can detect that the hatch is open, assumes that the car will be driven soon, and therefore some vehicle electronics will not enter their standby mode where current consumption is minimized.

Further, if your car has the Smart system then if the fob is within 15 feet or so of the car, the electronics current consumption will be increased by the fob continuing to communicate with the car, which results in the Smart ECU and body ECU drawing power, and possibly the skid control ECU also powering up in preparation for energizing the brake actuator pump.

Finally, if your 12V battery is in marginal condition to begin with, it won't take much of a current draw to get the battery to the point where it will not start the car. If you are camping it may not be that easy for you to get help at that point.

Therefore - if you really need to keep the rear hatch open for an extended period (several days) then I suggest you should disconnect the 12V battery negative cable where it bolts to the body.

 

...believe Feri is on the right track....
There are now at least 2 camping tents designed to fit on back of open hatch top Prius.
One is on EBAY (Habitents) and another one is at AutoAnything.com
Maybe someone who owns can say how they do this, or you could find instruction on-line.

Like Hybrids? Like Camping? You'll Love The Prius Tent

 

Like Pat says and I would get one of those 12 volt portable jump packs. I'd have one of those no matter what car I used if I was deep in the woods.Would be awful to get a dead battery deep in the woods.