No, it doesn't if the pot is burned red-clay (as they usually are). If it some other material than clay (red-clay), don't know... Test it first; Put water into two pail, measure boh water values. Then put the pot into one of the pail and keep it in for a week. After that measure water values and compare them together. They should be same, if the pot doesn't change values.
although you have to remember, if the pot contains CaCO3, CaCO3 doesn't dissolve in basic water.