First, not all beer is the same; some have a lot more calories (carbohydrates) than others. "Liquid Bread" was the term I learned when I was stationed in Germany. It referred to German brews, not US "lawn mowing" beer. So, In part, depends what type of beer it is.

Second, even with low carb beer, I don't think the intake of, say 12 US oz of fluid + at least some carbs, will cause you to lose more than 12 oz of liquid, so it is a net gain in liquid.

Heck yes, 1 beer each will help: now, a six pack all at once is a different question.