It can be done. I do not have running water in my printing area. I have to move prints to my bathroom to wash. It is not ideal, and it is a bit of a hassle, but works fine. I also process film in the bathroom.
When I was in Yellowstone one summer, I bootlegged a darkroom in my quarters. I held prints in a tray until morning, and washed everything in the shower the next day.
My biggest problem is that I cannot easily print during the day, due to light leaks. I can place something in front of the leaky sliding door if I *need* to print during the day, but it has to be something big, and has to be moved every time I go out to the bathroom to wash prints.
So, I would worry more about getting everything light tight more than being away from running water. Also, it helps if you rent, so you are not paying for all the water you will use!