This route was was my first experience with Class 3 and I found I was totally comfortable without any sort of protection, even with several inches of fresh snow in the chimney. The holds are very large and the exposure is moderate. Given the extra weight a rope and gear would add to a pack and the distance you would have to carry it up, my recommendation would be to leave the rope in the trunk. From what I have seen elsewhere, guided trips may rope up for this, but it seems like that is just out of an abundance of caution for their paying customers.
