If Arsenal defeats Barcelona, it is possible that can they go on to win the UEFA Champions League. However, Barcelona is currently beating Arsenal. If Barcelona wins, it could hurt the moral of Arsenal's team. Entering the UEFA Champions League with a lower sense of team pride could diminish Arsenal's chances of winning.
If Arsenal defeats Barcelona they would go on to win the UEFA Champions League because they are in the top 3 in the league as it stands. Given the season prior to this win, Arsenal has what it would take for them to go on and defeat the contenders for the championship.
Barcelona is easily the toughest competition that Arsenal has faced, and will face this season. If Arsenal is able to defeat Barcelona, there is no reason why they cannot win the UEFA Champions League. Barcelona has the strongest defensive game in the sport, in my opinion, and to surpass their defense would mark Arsenal as one of the strongest offenses in the game.
Arsenal are renowned for their constant 'bottle-job'ry and they always mess up when they should be winning. It is likely that in the next round they would get another top team and I just don't think that they have the quality to compete. They are playing the worst they have been this season and if they beat Barcelona then they would almost certainly be knocked out in the next round
While beating Barcelona would be a big step toward winning the UEFA Champions League, Arsenal have too many quality rivals to get through in order to win. They'd likely have to beat at least two of Real Madrid, Bayern Munich, Juventus, Atletico Madrid, or PSG. While Arsenal has a decent team compared to these other teams, it might be asking too much.