Yes! There are all the classic elements of a comedy which authors of the time knew would provoke laughter and merry-aking: a girl dressed as a boy, love interests, mistaken identity (which the audience would have loved), a shipwreck, inside jokes which include the audience, marriages at the end, comic wordplay throughtout, and nobody dies within the context of the play (if you don't consider all the souls lost when the ship actually sinks allowing our two stars and their servants to escape conveniently to the same island). Not to mention that the play was performed on January 6, 1600--the Twelfth Night from Christmas, and it was usually a very festive time of year celebrated with many parties and celebrations. In fact, Twelfth Night would have been considered in Shakespeare's time to be even more important than Christmas itself since this is the day believed to have been Jesus' baptism day.
The festival of the Epiphany on the twelfth day from Christmas was observed with numerous ceremonies which included performance of plays at Court. Shakespeare's play Twelfth Night was also presumably written for performance on Twelfth Night. It was one of four plays the performance of which before Queen Elizabeth in the Christmas season of 1601-02 is recorded.
Twelfth Night may be called a festive comedy primarily because of the occasion of its composition. In act2 sc.3, Sir Toby tells Olivia's steward, Malvolio, rather sarcastically, 'Dost thou think, because thou art virtuous, there shall be no cakes and ale?' This reference to 'cakes and ale' also relates the play to the festive occasion of Twelfth Night.
Olivia's 'allowed fool', Feste, bears a name that relates to the spirit of festivity & he proves himself to be one of the major sources of fun and mirth in the play. All the four songs are sung by him at different points of the play's action. In fact Feste's songs and Duke Orsino's love for music contribute to the festive character of the play in big way.
The play also accommodates such elements as mischief-making, witty repartees, gulling, disguise, adventures and exchanges of love and romance which build up an atmosphere of great fun and enjoyment.