During the ensuing fight the priest gets tied up in a sack, threatens to inform the police about the tinkers' poaching and is only released once he gives his word not to go to the police.
Yes, it is a farce. While it is quite funny it's not Synge's best work. He's probably best known for The Playboy of the Western World which also features violence.
Synge was a strong advocate for the Irish rural peasants despite his wealthy upper-class background, believing them to be a distinct and colourful class. He also believed that lurking not far beneath the surface of their avowed Christianity was a brutal paganism, hence the violence.
Synge rightly believed that The Tinkers' Wedding couldn't be performed in Dublin because it would be too upsetting for the Catholic population seeing a priest tied up in a sack, as there'd been a violent reaction when Playboy premiered, which kind of proves the point of a brutal undercurrent.
Reading the play, I could hear their lilting Anglo-Irish, their distinct phrasing which is delightful and their special humour. It could be fun to read this in the play reading group.