In a perfect world that would be great, but it won't take long for a predator to find them, not to mention if the water system breaks and your not aware. Just my opinion but I don't think it's a good idea for that length of time.
Besides the comb looking pretty red to me at this age, they both look like they have pointed feathers around their necks. Good indication of a cockerel.
There could be different causes. How old is the hen and what type. I would try mixing in some oyster shell with the feed. My hens never seemed to eat it if I just left it out but would if I mixed some in their feed. Maybe that will help.
She doesn't look normal in this photo. I would maybe treat for coccidiosis. I've had that happen with chicks before but not that young. I'm no expert, just someone who has raised chickens for a long time.