I don't know if stability of Bitcoin price would contribute for it to become more popular but I know that people like Bitcoin because of its volatility. This gives them opportunity to make some money and everyone likes money. I'm not sure that currency like Bitcoin could ever be stable that is just not the part of its nature.
But recently bitcoin value stay on $ 700 over a months , I can consider bitcoin popularity increased over a time
Let see the time goes on so more people can decide to invest bitcoin