This is an interesting question, and a tough one to answer. On the one hand, it would appear that the play is something of a comedy, and a romantic one at that: there's the courtship between Portia and Bassanio, humorous sequences (such as the ring prank during the end of Act 4 and in Act 5), and a seemingly happy ending without any loose ends. By all accounts, these seem to be the qualities of a romantic comedy.
On the other hand, we have Shylock. A controversial character, Shylock is tough to characterize. Is he a bloodthirsty villain rendered with blatant anti-Semitism, or is he a tragic victim, an individual assailed by the racism of his fellow Venetians? However you see him, one thing is clear: it's difficult to avoid sympathizing with Shylock. For example, in Act 3, Scene 1, Shylock struggles to establish his status as a human in the face of the prejudice that oppresses him, saying, "I am a Jew. Hath not a Jew / eyes?" (51-2) and "If you prick us, do we not bleed?" (57-8). This poignant speech is one of the most famous points in the whole play, and it helps the reader understand that members of the Jewish community in the play are viewed as more or less subhuman. With this idea in mind, Shylock becomes the most sympathetic and relatable character in the play, and it becomes very difficult to rejoice in his humiliation during the later courtroom scene.
To put it simply, there are elements of romantic comedy in the play, but there are also much darker layers hidden beneath the glittering, comedic facade. As such, one would be hard-pressed to call The Merchant of Venice a successful romantic comedy, as Shylock's complex character consistently destabilizes such an easy reading.