So, fermentation is complicated, and the answer to this question really depends on multiple factors. You're particularly interested in the role of sugar vs. salt, not lactobacillus vs. yeast. The simple answer to that question is that lactobacilli are salt-tolerant, while yeast is much less so. So adding salt gives the lactobacilli a headstart in converting the sugar present in your pre-pickles into lactic acid, and causes any yeast not killed by the salt to starve, and thus not produce much alcohol.
If you add more sugar on top of the salt, it won't cause alcohol production because the yeast will still be retarded by the salt, while the lactobacilli are not. You will just get really, REALLY sour pickles because the lactobacilli will convert all that extra sugar into acid as well.
That said, you can still get alcohol in your ferment. If you initially bite into a pickle and it's fizzy, that's a sign of alcohol. The yeast, while slowed down, is still going to grab some sugar for itself at the beginning and produce both alcohol and carbon dioxide. So carbonation itself is a sign that there is alcohol in your ferment.
That doesn't mean it's strong enough to make you feel anything, but it's important to remember if anyone consuming the ferment is on probation, or young, or pregnant, or a tee-totaler, or anything else you can think of. I've heard stories of children going to the hospital with high blood alcohol from drinking too much water kefir -- which is NOT a salty lacto-ferment, but still makes a point worth considering. I also know someone who failed a mandatory blood test because she drank kombucha, characterized by acetic acid and friends, not realizing that it could contain trace amounts of alcohol (luckily she managed to explain things and get out of trouble).
So, if you wanted to have an alcoholic pickle, you'd want to 1) leave out the salt, 2) inoculate with yeast to ensure that lactobacillus (or assorted nightmare bugs) don't manage to outcompete the naturally present yeasts, and 3) control the oxygen present. Adding sugar should be optional, but would be recommended I think.
[I don't drink alcohol, personally, so I wouldn't know, but I think if you're drinking pickle-born booze, you'll either want it sweet or really, really strong. That way you either won't have to taste it or won't have to think about it very long.]
I should also point out I don't make explicitly alcoholic ferments, so I'm not a practiced expert. But, the general rule is that you should initially use an aerobic ferment before introducing an airlock and creating an anaerobic environment. That's for two reasons. The first is that yeast can use both oxygen and sugar to produce alcohol, but only require sugar. So, Initially, to get the best of both worlds, you allow the yeast both. However, after a short period of time, if continually exposed to oxygen, the newly produced alcohol will start being converted into acetic acid by other bacteria. That means vinegar. If you take away the oxygen, vinegar doesn't happen.
That's why kombucha and kefir, for example don't become strongly alcoholic since they ferment entirely in an aerobic environment. Alcohol IS produced by the yeast, but is then in turn converted into various acids by the various strains of bacteria present. This is also why many people choose to perform a secondary ferment with kombucha and beer (although I only know kombucha thoroughly), where they add more sugar, in the form of fruit or flavorings, then cut off the oxygen supply and let the yeast work for a few days while many of the acid-producing bacteria take a backseat. This produces a fizzier drink, which indicates increased alcohol production. Kombucha is still very mild compared to other drinks that are intended to be alcoholic, but it's still worth remembering.