DererkRI had the question correct, I was wondering if it is "possible" or if anyone had some secret to do it. Ya know, to try something different. I think that the Harlequin wrap would probably be the closest, but like I said it is not for me.
I always switch directions mid wrap to make both the top and bottom wrapped areas self-tightening on my road bike. I have had problems with the wrap coming loose on the top of my bars before, when I didn't reverse the wrap. I guess I pull hard on the bars. That is where this line of thinking came from.
Anyways, I wrapped the bars last night all in one directions as tight as I could. I will see how well this last. From all of the responses, I am assuming everything will be fine.