Whether they can live depends if the nitrogen levels stay healthy (assuming your substrate doesn't leach ammonia/ammonium or much nitrates and that you can use a cycled filter in that low water level) and you provide surface agitation. They can tolerate a wide range of temps, so as long as it's not too drastic.
Shrimp will stress the same as fish, the more things are out of their preference range, the less likely they will be happy enough to breed successfully or even be healthy. I know that fish can get stressed with low water levels (they sense they are in danger of a drought), I am not completely sure if shrimp do too, but I would assume so. The low water level is a low water volume and so it has less dilution potential of nitrogen levels so they can feel the toxic effects of nitrogen since it reaches higher levels than it normally would in a large body of water. Less water volume also has less stable water temperature so their body has to deal with fluctuating temps (unless your house is heated and stays rather stable 24/7). The low water level in itself decreases space (vertical) so that may be a factor as well. The point I am getting to is that if the shrimp are happy enough (which there are a whole lot of factors) they will breed readily, but the more out of their preference range/more stressors their body has to deal with the slower they will breed or not breed at all. I can't say for sure whether or not they will breed in those conditions, but if you can use a filter (for nitrification and oxygen) and the temps stay relatively stable, they should still breed (assuming the other water parameters are suitable) albeit probably not as fast as they would in a even better environment. Then again they might not breed at all, as it can sometimes take months before shrimp settle into a new environment and start feeling comfortable enough to start breeding, or maybe they would breed, but the females would get stressed out and drop eggs. Just reasoning it out. As long as the shrimp would survive in that set up, you can just try it out.
By the way, what fish would you be stocking? Are they big enough to eat the adult shrimp?
Mind the nutrient levels as well if you are dosing or your substrate leaches, as the water volume is low so ppm can build up and may be too high/hard for the shrimp's exoskeleton.