Absolutely but Brain Stew is one of the easiest songs you will likely ever learn.  They are generally easy as they stick the same chord progression, the tricker part in the beginning is getting the strumming down.  The entire American Idiot album is fun to learn, notably Wake Me Up When September Ends (fun to switch between acoustic tones and electric plus it has a fun solo that is pretty straight forward).  Jesus of Suburbia is also fun but very long so good for practicing the memory.  The thing about Billie Joe Armstrong and he readily admits it, the guitars in their songs for us average players.  They don't require crazy shredding, tapping, pinch harmonics, etc. just melodic and fun to play.  Guitar Hero with a real instrument.