I would imaging that you get a little surface flavor but since they are already dry the cells are pretty much closed for business. If you added some moisture to the beginning of the smoking process and then removed the moisture you could get a little re-hydration happening, infuse the smoke and then dry them again.
Yes you want to smoke while the peppers are still fresh. You also want to watch your temperature as you can also end up cooking your peppers. Once you've smoked your peppers for your preferred length of time, finish them off in your dehydrator, food dryer, or simply put them on a rack in front of a fan in a reasonably warm area. I use the kitchen counter.