No. The best epidurals are when the patient is not experiencing pain but is still able to push effectively. The anesthesia provider will work with you to get your pain under control, but the amount of pain relief can vary from person to person. Sometimes patients are not pain free. Sometimes patients are so numb they can not push very well.
Surgery or delivery? If you are asking about an epidural for surgery, you should not feel pain. The epidural needle and/or catheter will be injected with local anesthetic before surgery. More local anesthetic and/or narcotic will be given if needed. If you are asking about epidural for childbirth, you will probably feel some pain as the medication is adjusted to balance pain relief with the ability to feel and push.