No. I have literally never heard the word "birdbag" until you mentioned it. "Birdbrain" is common and understood, but it is slang and it's also very disrespectful. Although I do check urbandictionary occasionally, it is NOT RELIABLE. It's full of made-up words and "dysphemisms" (words that have been deliberately made into WORSE words by making them obscene). urbandictionary is NOT your secret reliable guide to the "real English." Check anything you see in urbandictionary against a real dictionary. It should show up in the real dictionary, perhaps labeled "vulgar slang." If it doesn't, then it is either made up, rare, or local. Finally, be aware that "bag" has a number of nasty overtones--"scrotum" or "testicles" and "douchebag"--and sometimes it used in slang expressions just to give them a little bit of extra nastiness.