Sounds good to me! I love combining transportation and exercise, it's so efficient. This is a bit unusual but it will get you the training you need.

The only thing I've done that is running for transportation is that I run 1 mile to the pool, swim, and run the mile home. I tuck my swim cap in my tights, goggles around my neck, carry a water bottle and towel. When I did that it was cold enough for a jacket so I put my underwear in a pocket. On the way home I carried the swimsuit as well as the towel. I don't know how I'll transport the underwear in the summer when I don't need a jacket. I'm not wild about just carrying my underwear. The only problem I have had so far is that one time my swim cap fell out. I swam without it and found it on my way home.

Let us know how it goes.