Nor was it the case in the European Cup, since goals scored away are doubled in case of a draw
It seems like nothing can prevent Barça from going through to the Champion's League quarter-finals. Not only they're displaying a fantastic level and have already totaled 33 games unbeaten, but the statistics also predict an elimination from the Champion's League for Arsenal.
According to the figures published by MisterChip on his Twitter account, since away goals are worth double in case of a draw, there were 347 European duels (all competitions are concerned) with a 0-2 result in the first leg. Of those 347 games the loser has come back only 9 times in the second leg (3% of the cases). In the remaining 97%, the team that won the first leg went through to the next round.
If we only take the European Cup as a reference (in its previous form as well as the Champion's League), this happened 85 times. The 0-2 lead was never overcome in the second leg.
In all European competitions, 10 English teams (like Arsenal) lost the first leg by a 2 or more goals margin. None of those teams could come back.
The only negative precedent in Barça's history was the first draw of the 'Cup Winners' Cup' in 1984/85. After winning against Metz by 2 goals (2-4), the French team won in Camp Nou 1-4 and eliminated the Blaugranas. It is the only time Barça was eliminated in a European competition after having won the first leg away from home by 2 or more goals.