"The beer, please."
Translation:את הבירה, בבקשה.
Short answer: Yes. Long answer: Sentence fragments are tricky - you have to always make it into a full sentence to properly understand. Try turning the English into a full sentence like "Pass me the beer, please", or "what do you want?" "the beer please" (which would then be short for "I want the beer, please"). Then it becomes clear that beer is a direct object.
You could say בבקשה or בירה בבקשה , but those sentence fragments are different than this one. The word את is grammatically a preposition, which is why it cannot be implied. An analogous English exampjle is when you present someone with something and say "for you." If you just said "you" that would be confusing. In slang, את הבירה בבקשה sounds more like "tabira vaksha". So at a bar, you'd probably say that - but at a catered dinner, you'd say the whole thing.