I have epilepsy and no, it cannot be cured. Many epileptics are fortunate enough to have their seizures either completely or almost completely controlled by medication, but the medicines treat the symptoms; they do not cure the condition.
Sometimes a person will stop suffering from seizures due to changes in their body chemistry, lifestyle, etc., and can stop taking medication. However, that is the exception, not the rule. Most need to take medication for the rest of their lives.