If there's a field of medicine that deals with this issue more than any other, it's emergency medical services. Drunks are a daily staple for them, even in "nice" communities. So the following is based on my previous EMS training.
It is always unethical not to do an adequate medical assessment, but that doesn't mean you have to treat the thing they're complaining about.
First, if they're heavily intoxicated then that means they cannot give informed consent. They are not considered mentally competent to make health care decisions under US case law; I expect it's similar in other western countries. So they became your responsibility the minute you recognized their mental incompetence (failing to recognize it is just as bad).
Second, if they're intoxicated then that can mask and/or mimic other concurrent issues. Refusing to at least examine and rule out other problems is therefore negligence. More than one police department has paid a heavy price for jailing "drunks" who were in fact diabetics in insulin shock. Intoxication also dulls pain, so even their own pain assessments can't be trusted.
Finally, how intoxicated are they? Remember, being intoxicated means they are your legal and ethical responsibility. Until you've done an adequate assessment to determine that they are mentally competent and not suffering from concealed problems, refusing care will most likely be judged negligence by both medical and legal authorities.
Intoxicated people (by any substance) are the quickest ticket known to loss of license and negligence suits.