Without culinary training, is it uncouth for someone such as myself to visit a restaurant in off-peak hours and ask to speak to the chef, and then in turn ask if I can work in the kitchen?
Sub-questions: 1. Is there a better way to go about this?
2. Will I just be washing dishes for months and months before doing anything related to actual cooking?
3. Is there no way in hell this would ever happen, but for perhaps working the salad bar at the local Olive Garden?
Main question: that's not uncouth at all - happens all the time. You may not want to use the title "chef". Just say what you want to do and let them tell you who you should talk to - it could be a GM, Sous Chef, whatever.
Sub 1. Your way is decent, but you might also consider the fact taht your first stint really doesn't need to be "high end". More than any real cooking technique, you need to learn the about the fast pace, the sometimes unbearable heat, the foul language, and the damage a knife wound can do. You can learn all of those things at a hole in the wall diner just as well as at Charle Trotters. And Trotter and others would respect you more and be more likely to hire you if you came from said hold-in-the-wall diner.
Sub 2. Depends. Is mopping the floor more or less related to actual cooking than washing dishes? Don't ask this question if you want the job.
Sub 3. It could happen if you're willing to work your tail off and don't come across as the slightest bit "deserving".