The thing is, this is not going to happen next week. How long do you have to get them in some semblence of shape? Six months?

There's a lot of improvement that can be made in six months. A lot will depend on an appropriate program that (a) is effective at improving fitness and endurance (b) meets their time contraints and (c) keeps them motivated.

It may evolve OK, or not. It depends on who is in charge and what their expectations are.

But the relay idea is as effective in just about all respects because it bonds employees, there is an equal level of self-achievement (that is, no-one is likely to not complete the allotted distance and therefore feel a failure, and hence not be a part of the group bonding), and the image of the company may be enhanced by complete success (or at least not affected negatively by demotivated participants, people taking a week or more off afterwards to recover, and the real possibility of crashing, injury or death).

I can see both sides of the discussion.