If your female mouse died will the other female that was with her be all right or will she get depressed?

It is possible. Bored is probably more like it, because there is nothing to do when you are not around to interact with it. But be careful, because that rationale will result in you replacing rats for the rest of your life. Decide if you really want another one, and don't feel guilty if you decide you don't. Rats don't live all that long, as I recall, so the situation is not likely to go on and on.