On PS3, at least. Not only does playing a song on RB3 count towards goals, but it counts *separately* from playing the same song in Blitz.
Which is to say, once you find the three songs on the Blitz soundtrack that qualify and play them in Blitz, you then play two of them in RB3 and shazam (after the RB3 DB syncs with Rock Band World, which seems to be once a day now) - goal completed.
RB3 play also gets around the 'no duplicates' rule in other goals as well. I played Wicker Man in Blitz twice but only one of them counted towards the Iron Maiden stars goal, but I then played Powerslave once in Blitz and once in RB3 and each one gave me credit towards the goal.