I hate to "kill the buzz"...
One of the main signs of an alcohol problem is the persistence of drinking despite consequences, and denial. I'm in recovery, so I feel I have a degree of experience and knowledge with which to draw on 🙄
You can't always smell alcohol--I was able to hide my drinking (and use of other drugs as well) quite effectively. People can hide it, so that's not the main factor. In addition, just b/c you go to the interview drunk or hungover doesn't necessarily qualify you as an alcoholic.
A key aspect to addiction is the idea of choice. Even better stated, addictions are defined by the decreasing lack of choice, and increasing power of the addiction and subsequent consequences on the addict's life. Despite the consequences, the addict cannot, on his or her own, abstain from the behavior or substance. Instead, the addict will find ways to protect the addiction. I personally became an expert at lying and hiding it well. Or, when I had a seizure b/c of severe dehydration linked with my alcoholism, I resolved to buy Gatorade. As a crude analogy, it would be like giving a patient with clogged arteries some blood pressure Rx's, instead of performing surgery to remove the clogging....
I'd prefer someone to have a dismal interview due to being drunk/hungover, b/c it's an opportunity for them to see how their substance abuse is effecting their lives. It is more likely they will enter recovery.
But let's say you do well in the interview and get in. If you are an alcoholic, you'll say, "See, I don't have a problem (or, see, I can handle my problem). I can keep drinking..." Not everyone with an issue like this experiences consequences right away, hence the term functional alcoholic.
Obviously, there's issues down the road of safety and ethics and whatnot about performing under the influence. But this is not a good reason for recovery. It must be out of a desire to really live your life to the fullest. It must be out of self respect; b/c you want a better life for yourself. If you want to be sober for any other reason, you will relapse. Moreover, you SHOULD relapse, b/c recovery is more than just eliminating consequences and being more acceptable to other. I don't believe in lecturing people about the evils of addiction. Do it for yourself first, and you will be a better doctor second. Recovery is awesome--I haven't looked back at all. I wouldn't trade it for anything in the world.