Accomplishing personal goals, I believe, is vital for your psyche. It is easy to see how corporate support to achieve personal goals could increase morale - That is, if my dayjob paid all my hotels, spend work hours planning for the trip, etc. And certainly, had this been part of my job, I would probably spend work hours finding similar businesses to hook up with during my trip.
But be careful: It would be tempting to upgrade my bicycle to an electric one. It wouldn't be the same. I would spend more time stopping than riding, and I already spend about half my bicycling time doing other things than bicycling. It would feel more planned and with less freedom.
In short, as long as everything was in my own hands for the entirety of the trip, I was energized by self realization. This, in contrast to my trip to New Zealand about ten years ago, when I had this "wow, how did I end up on the other side of the planet, how cool is that?" form of self realization the first couple of days until work wore it off.
So the key leans more towards self realization than accomplishing the actual goal. In other words: support, but do not interfere. Or in the words of Dan Pink: You probably want to do something interesting, let me get out of your way.
Completing my mission motivated my wife to bake :)