Any fermented liquid can contain "some" alcohol... that's just a natural by-product of fermentation with yeast. I've measured the ABV in my ginger beers at about 1/2-1% between various batches with a hydrometer but have never felt an alcoholic effect from them.
I would hazard a guess that, so...
I've been maintaining a ginger bug going on three years now and have not done anything other than semi-regular feedings with white sugar. My bug was started with about 500g raw ginger, half of it sliced and the other half chopped through a food processor to increase the surface area of ginger to...