I would say depends on the chef. Back when Marco Pierre White was actually cooking and had his Michelin Stars he claimed to have been in the kitchen practically the whole time. On the other hand you have Wolfgang Puck with his dozens of various outlets, chains, restaurants, books, TV appearances, etc. In that case I seriously doubt he spends much time at his restaurants (even Spago) and is preoccupied with other stuff. As for Mario Batali, who knows? But you should know that he's been a TV personality for a long time and that most of the more mundane kitchen duties that a chef has to contend with have been handled by his extremely capable and competent chef de cuisines, sous chefs and cooks for years in his various restaurants. However, at that point in the game they might start to do more work in the front of the house, smoozing with guests, signing autographs or what not. I'm not a celebrity chef, I don't know what they do during the course of a year and I can only guess.
"If it's chicken, chicken a la king. If it's fish, fish a la king. If it's turkey, fish a la king." -Bender