When you're intoxicated you can be charged with a crime of public intoxication and be charged with carrying a firearm while intoxicated so yes it is illegal to carry a firearm when you're intoxicated or even on other drugs.
Carrying a firearm while intoxicated can be dangerous and you may end up shooting and killing someone even if you didn't mean too.
When you're intoxicated you can't control what you're doing so it's a good thing that it's illegal to carry a firearm while intoxicated.
Most places even prohibit people from carrying a gun into any bars or establishments that serve alcohol.