No, the only way BTC will get less volatile is if it actually starts having a real economy develop using it. Right now, only a few get paid in BTC for their work and can purchase all of their wants and needs with BTC. Even many people who manage to cover most of their expenses with BTC alone, actually rely on some method which converts the BTC to fiat.
I'm not actually sure that will dampen volatility. It would remove selling pressure from the market since people would no longer need to convert BTC to fiat. But removing that liquidity from the market could actually make the market
more volatile, since it will take less capital to push the price up.
I am not convinced that BTC can really sustain an actual economy. Since it is limited in supply, this encourages hoarding. If too many people HODL, that is not much money flowing and makes for a poor economy. BCH and Lightning network claim to solves this by making the scaling better. However, if you just build bigger pipes, but you only have a trickle worth of water; you are still going to get only a trickle.
I think you might be right. It boils down to Gresham's law. As long as bad money is still in circulation, people will have incentive to hoard BTC rather than spend it.