If possible, it would be good to determine the cause of the split. If it split because of dropping or other similar physical cause clamping and gluing the split should work well. If it is split because of wood movement, then you should rectify that, if possible, otherwise the split will recur, glue or no glue.
Movement is a fact of life for wood, while heating and cooling seasons make it worse, it will always move in reaction to the relative humidity, and the assembly needs to accomodate that. For example, does it have metal corner pieces that keep the wood from moving?