If I sign a noterized legal document while under the influence is that document still legal?
You can sign anything but whether or not it is binding - or will hold up in court - is another story.
For a contract, in order to be bound to a it, the parties must be competent to enter into such a legal arrangement. Underage persons, persons who are mentally ill, and intoxicated persons are usually not held to the contracts they enter. However, a minor may have the option of enforcing a contract.
As for a Will, you need to have "testamentary capacity" in order for it to be binding: know who your heirs are, etc.
If you signed something and you now regret doing so would seek legal help in your area. Good luck.