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)
Actually, the prices will be always swinging. Yes, probably the market will not show such great and deep falls but the volatility will remain its main characteristics.