yes it can. ivy is hardy and as long as the house is keep at an average tempature in your home and not in a window that has the hotest sunlight of the day. I have ivy and other vine trimmings that I leave in water until they grow root then I plant in dirt. Sometimes it takes longer than a week.
No doubt about it. My Ivy plant has been in water for 2 years. I keep it in the kitchen by my window, in a silver container. It's as healthy as anything and I don't have to fuss with soil. All I do is give it more water once a week. It's gorgeous.