Nope.
[Image from an American Seating ad circa 1959.]

seen from Germany
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seen from United Kingdom

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seen from South Africa
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seen from Maldives
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Nope.
[Image from an American Seating ad circa 1959.]
Now of course we all know that correlation does not mean causation and further testing is needed to come to any definitive conclusion, but still. I think it's fair to say that hiking is good for the brain as well as the body and soul.
This excellent guide for creating schoolyard habitats has tons of useful information about habitat elements, design procedures, and organization of habitat construction, use and maintenance within the school. Put together by the Texas Parks and Wildlife Department and the USFWS, there is also a series of appendices with specific information on for different Texas bioregions. If you want to plan a schoolyard habitat but aren't in Texas, I recommend reading it anyway--I think you'll find it very useful.
Here is a list (with descriptions) of a number of articles, resources, and research on the need for and benefits of connecting kids to nature. Just in case you need to prove your point to somebody.
Compiled by the Texas Parks and Wildlife Department.
Children playing at the awe-inspiring Glamis Adventure Playground.
Children and Nature Design Principles
David Sobel's Childhood and Nature: Design Principles for Educators describes necessary design principles for creating effective and engaging environmental and place-based education opportunities for children.
Adventure: introducing a sense of adventure into a learning experience places emphasis on children's natural desire to physically engage and learn through exploration.
Fantasy and Imagination: creating imaginary worlds or scenarios allows children to learn history, social studies, or other concepts through simulated experience
Animal Allies: children should be allowed to create meaningful connections with animals--whether through care and interest, or through animal role-play--both to develop empathy and to create a strong foundation for conservation education later on
Maps and Paths: beyond the developing visual-spatial skills, allowing children to explore and create maps of their neighborhoods opens the door for deep-rooted connections to human and natural places
Special Places: forts, tree houses, etc allow children to take control over their own spaces, constructing architecture and societies as they see fit
Small Worlds: scale simulations--whether maps, models, or dioramas-- allow children to literally see the "whole picture" of a complex system, such as a watershed or ecosystem
Hunting and Gathering: children desire to hunt and gather innately-- whether seeking treasure, tracking animals, gathering seeds, or collecting rocks. Educators can capture this enthusiasm to create fruitful learning natural experiences for children
Here is a set of design guidelines for creating natural play spaces that both serve the needs of children and support conservation efforts.
This comes from the Green Hearts Institute for Nature in Childhood, a group working to encourage and develop opportunities for childhood interactions with nature.
Over Thanksgiving I was checking out In Other Words Bookstore (the Portland feminist bookstore lampooned by IFC's Portlandia--though I promise the people who work there in real life are really very nice!), where I found the awesome nonprofit publication Rethinking Schools. This magazine, 25 years running, explores diverse topics of education, paying particular attention to student populations who are often the most overlooked.
This article explores the shortfalls of Richard Louv's idea of "Nature Deficit Disorder," pointing instead to more nuanced and inclusive ideas about how to teach environmental education and allow students to experience nature, particularly in urban schools.