In the past, I was a pretty extreme caffeine addict. Nowadays I drink coffee in relatively moderate amounts for most of the year, and then as backpacking season approaches, I gradually taper off to zero. My experience is that the amount of caffeine I need in order to function in the morning is simply whatever amount my body is used to. If I get my body used to needing zero, then zero is the amount I need in order to function in the morning.
I actually find it easier to go without caffeine while backpacking than while in civilization. Your body can't sleep while its large muscles are working, so, e.g., if you're ever having trouble staying awake in a darkened movie theater, a trick that helps is to swing a leg back and forth gently. Sitting at a desk in an office in the afternoon, I tend to get sleepy around 3 pm and feel like I need a cup of coffee. But when I'm out on the trail walking, that just doesn't happen.
Unless you want to feel really sick and miserable during your hike, I would suggest not trying to go cold turkey starting at the trailhead.