Microwave ovens cook because the frequency of the radiation in the magnetron excites (vibrates) molecules in the food. Radar uses a similar frequency to that in your domestic microwave (but is very effectively shielded to stop that radiation escaping). If you choose to stand in front of a ships radar, you will be badly burnt and possibly die if you don't get out of the way quick enough. You will be cooked (ie burnt).

Now, aircraft radar backscatter would be trivial compared to the radiation in front of it, but I am curious how much actually does go backwards and into the cabin. For all I know, it may be so slight that it hardly is measurable at all. Cosmic radiation (from outer space) may be a much greater hazard (and that IS documented as a hazard to crew).