I doubt you'll end up with the result you mention m1k3. That's a tiny amount of honey made up to 5 gallons. Honey isn't like any mash. It's 100% fermentable and if there's enough nutrition that the live yeast can get from the yeast cake, then it will more likely ferment dry.
Don't forget, with beers/mash etc, any residual sweetness is usually unfermentable sugars - you won't have any of that at the moment.........
I'd have thought you'd just get a lower strength dry batch.........
Might be wrong but I don't think so.......