Yes with mass adoption the stability in price of bitcoin will occur, but make sure that this adoption will not be for the purpose of holding and trading and wishing for ups and downs, but for the normal use, then is possible that bitcoin stability occur, otherwise if people adopt it just for ups and downs, nothing good will happen.
it depend on what stability you're talking about, perfect stability it's not possible, especially if yout ak einto account the massive usage that will happen in the future, if you want stability, this already will cause huge swings