So roommates and I tried this back in college - 'cuz we just knew we'd have more female attention than we would know what to do with when we pulled it off. Err, made alcoholic rootbeer.
We had several brew sessions under our belts at that point (7 - 10 if I remeber correctly) but were still brewing in the plastic starter fermenter. Our homebrew shop sold many flavorings and extracts for making licquor (mix with vodka) and sodas, and we picked up an ale yeast (dry) and a bottle of the rootbeer soda extract. Not caring about the flavor from the fermentables, we got bags of sugar from the grocery store.
It all went well enough to start: sugar, water, yeast, rootbeer extract and furious activity in the airlock - for an hour or two. Then nothing. We even set the fermenter in a tub of warm water to try to rouse the yeast. No luck. Went back to the homebrew store and puchased more yeast (at the suggestion of the clerk, mind you) and nutrient. Tried pitching that, with the same effect.
On further discussion with LHBS staff, we all realized that the soda extracts PURPOSEFULLY KILL YEAST after a short time to prevent bottle bombs. If you mix this stuff up with the intention of creating soda and bottle it immediately, you'll have enough lifespan to carbonate but not detonate, while retaining plenty of sweetness. We would likely have been ok had we added the flavoring after primary fermentation was complete.
Alas, the co-eds were to be disappointed. We didn't want to risk another failed batch on our limited budget, and so called our grand experiment a failure and moved on.
To keep a long story from getting too much longer: We poured the batch out, but the plastic tub was stained with rootbeer odor. Our next 2 batches had a varying degree of rootbeer aroma, which actually garnered many compliments (one was a brown ale, IIRC). So I can't say it was a total loss.
If I were to try again, I'd probably try to find a strain of yeast with low alcohol tolerance and keep it fermenting until it couldn't tolerate any more. I'd then add sugar to backsweeten, dump in the flavoring and force carb it. If bottling, I'd look to add some potassium sorbate. See this thread:
https://www.homebrewtalk.com/f30/potassium-sorbate-backsweeten-123599/