Nope.
In the Danish, the moment you start freaking about about preventing yourself from getting an isolate pawn, you're losing. I mean, you're already down a pawn. You lose the endgame anyway. Who cares if one of your remaining pawns is weak? Plus Bxc3 bc opens the c1-a3 diagonal, and your bishop may find a nice home on a3 (particularly when there's no black dark-squared bishop to oppose it. If he wants to give up a bishop for a night in an open position, you let him.
4. ... Bb4 5.Nf3
Now you'll usually see 5. ... Nc6 6.Bc4 Qe7 7.0-0 with a solid developmnet advantage for the extra pawn.
By playing this way with Nc6, Bb4, and d6, black plays into the main lines of the Goring Gambit accepted. Theoretically, this is fine for black. Practically? You'll score very well from this position, and learn a lot, too. You'll struggle until you break the habit of looking at moves like Bd2, but then your results will skyrocket.