Can a dry cell battery be recharged?

Some wet cells can be recharged (e.g. lead acid cell) some wet cells can't be recharged (e.g. gravity cell).

Some dry cells can be recharged (e.g. NiMH cell) some wet cells can't be recharged (e.g. carbon zinc cell).

It depends on the cell chemistry not the wet/dry construction. Also any wet cell can be made into a dry cell by absorbing the wet electrolyte into something and making a damp paste electrolyte.