Economic growth will most likely cause the price of bitcoin's to appreciate, but at a stable rate. Compared with the unstable movements of the recent past.
Bitcoins might appreciate at a stable rate in the far, far future when the currency is reasonably distributed. However, as bitcoin is attempting to replace fiat currency, a stable appreciation is highly unrealistic until it is already mostly adopted by those who would adopt it.
Actually, the great depression has its roots in the underlying medium being too "hard" like bitcoin, and the recent recession definitely has its roots in being too "soft" like current fiat currency (mostly because of 10% fractional reserve, but also because of deregulation). Hard currencies are open to manipulation by wealth-holders--incur deflation by hoarding, spend cheaply. Soft currencies are open to manipulation by governments and banks. The austrian school of thought wants to remove government manipulation as they believe this is the cause of the business cycle. Mises recognized that a hard currency had many faults, he just believed it was better than soft currency managed by government.
Why not get rid of both problems?