Chad, it could add some weight and stiffen up the dynamic spine quite a bit.
I was just re-adjusting some of my arrow spine worksheets on Stu's computer and in the past just entered 5" 3-fletch. This time I weighed a bare shaft on my reloading scale. Then I added a One-stringer 9" wrap. Finally, I fletched it up and re-weighed. Came to a total of 30gr increase, so I entered "other" in the fletching block and 30gr for actual weight. The dynamic spine showed an increase.
All of the electrical heat shrink tubing I've used in electronics work has been pretty substantial compared to the thin film One-Stringer wrap, so I would expect an even greater increase in dynamic spine.
It will be interesting to see what you come up with.