I have a very small half bath that I never use and probably never will as long as I live in this house. The tank on the stool is leaking so the floor under it is destroyed. I tried shutting off the water to the tank several months ago but the shut-off doesn't work. I have someone coming to replace the floor and would like to have him put in a new stool but not hook water up to it. I don't want to have to keep this clean and free of hard water deposits. Will I have any kind of problem such as sewer gas coming into the house if I do this? Is there an alternative solution?

Sewer gas would emerge under the circumstances you cite. Anywhere between the stool and the main sanitary drain you could cut into and cap the drain that services the commode. It seems wiser however to replace the commode and keep it operational.

Pour about a quart of cooking oil in the bowel. That will seal the drain and keep sewer gasses out and but will not evaporate like water.