Generally no, but it might depend on a cell. If a B cell is triggered into differentiating (the process of maturation) then it can later become a plasma cell, whose sole purpose in life is to divide and make antibodies. But the division is not part of the maturation – the cell is already mature when it divides.

However, as a rule of thumb, differentiation is the structural specialization of the cell to better fulfill a function or another. I don’t think this definition can include any type of cell division.