I started no dig in 2014 and my experience is that the slug problem is partly decreased by not digging, but by far the biggest parameters are good compost (eliminates almost all slugs on a no-dig bed with reasonable sunlight) and good sunlight (even good compost does not totally eliminate slugs on a no-dig bed with less sunshine).
I have four 5m*1.5m beds in good sunlight and this year, with good compost, they are all slug free.
I have two 3m*1.25m beds with partial shady conditions and even with good compost, most crops have had some slug damage (carrots, cabbage, pea shoots, dwarf bean, tree spinach, tomato). Beer traps helped with carrots, less good for the others even though the beer killed plenty.
As 2017 is the first year I had good amounts of high quality compost, I can say that not digging in 2015 and 2016 was not sufficient to eliminate slugs, including damage to turnips, radish, peas, dwarf beans, lettuce, cabbage, kale, pak choi and carrots. I ascribe this to lack of sufficient amounts of high quality compost, although I am also certain that not digging does help too…..