Reality check: sometimes, when slowly grinding up a hill on a mountain bike, I ask myself "wouldn't this be faster if I didn't have to drag this bike and was just walking/running/hiking?"
The answer: no.
That is, not if you're carrying a heavy backpack. Case in point, a backpacking trip in Great Smoky Mountain National Park.
18 miles. 9 hours. Biking is faster. My quads are destroyed. So please, for the love of Pirate, stay on the bike. Don't get off the bike.