I think so , if btc going to substitute with existing currencies , its value will fix or fluctuates will be less. and also there is another parameter : amount of btc. as you know it is 21.000.000 pieces.
after all btc be on market this also makes stabilization I think. ( But it is going to take so long time)
I agree to that, when the time comes that it will be reached it's globalize adaptation it will possible that bitcoin can produce lesser fluctuations and makes a little bit possibility that it could be make a fixed value. However, in other hand it's hard to think and I have a doubt that it will fixed it's value because as we remember this system form to be decentralized and no one's can control it so I think it will steadily what fluctuations it has for now and in the future. But will never know and maybe it will happen or not the most important is we can benefited from here and it will last forever.