Main financial function of gold is to determine real value of fiat money. Because fiat money is backed by or is based on gold. If bitcoin can determine real value of fiat money better than gold, yes bitcoin can replace this function of gold.
Bitcoin can perform this function better than gold. Because bitcoin quantity is known more precisely, can be monitored easier and faster. So, scarcity of bitcoin is provable with less doubts than scarcity of gold. Therefore bitcoin represents base value better than gold.
It means, in the future, after bitcoin value becomes more stable, we may have to use bitcoin value to calculate real inflation and to compare price movements in the past and to estimate future value of investments. Bitcoin can slowly replace fiat money too, if this happens. Because bitcoin doesn't have inflation and doesn't have the drawbacks of gold if used as a means of exchange in daily life.