I've been a vegetarian for 14 years, so I don't exactly recall what my concentration was like before vs. after (and I was a teenager before, so I was probably only concentrating on girls and rock and roll, but mostly girls). I do know that it isn't uncommon for testosterone levels to be reduced in men who become vegetarian, depending on diet, which actually has an adverse effect on many aspects of life including concentration. However, with a small amount of care, it is very easy to eat a vegetarian diet that is entirely positive for health. Walnuts (among other tree nuts and legumes), for example, provide the building blocks of testosterone better than the vast majority of animal products.
I think, in general, we have a pretty poor understanding of how various foods interact with the human body, particularly foods that trigger hormone production (as many high density proteins, like meats and non-tofu soy products, do). So, I would probably agree that a well-balanced vegetarian diet probably does lead to a more balanced day-to-day emotional life, which helps with concentration, wakefulness, and feeling good about what you're doing with your life (which I find is the single most important aspect of productivity for me).
I certainly encourage folks to give it a try, and see how it works for you. But do some reading first. There are some non-intuitive aspects that throw new vegetarians for a loop, and make the experience less than satisfying. For example, soy proteins of some types, while they seem like a high quality protein, are actually rather hard for your body to deal with. Tofu, on the other hand, which is processed similarly to cheese, has had those hormone-related proteins broken down into a form very friendly for your body.
I've also known people who've become vegetarian and gained weight (which was not my experience, as I lost about 15 pounds within months of becoming vegetarian without trying), because they've become carb-o-terians or bean-and-cheese-a-terians. Even if you rule out a whole class of (predominantly) unhealthy food in the form of meat, you can still eat a phenomenally unhealthy diet. And being unhealthy is bad for concentration (among other things).