There are two pseudo-Chaucerian texts of "The Plowman's Tale," but the one published around 1400 made it into "The Works of Chaucer." Later a Prologue was added in the 1500s to make it fit better into "The Canterbury Tales." However, a traveler with none of the characteristics of Chaucer's plowman is in it. Chaucer's plowman was a decent lower-class pilgrim who treats his neighbor fairly and pays his church tithes and taxes. He lives simply, with wisdom and strength for stamina. Chaucer characterizes him:

He would thresh, and thereto dike and delve /For Christe's sake, for every poore wight,/Withouten hire, if it lay in his might.

Does the Plowman have a tale in Chaucer's The Canterbury Tales?

The Plowman does not have a tale in Chaucer's Canterbury Tales. There have been several stories by writers other than Chaucer that claimed to be the Plowman's tale in the fifteenth and sixteenth centuries, though. At least one of these made it briefly into print during that time period. 

Although the Plowman is one of several characters in the General Prologue not to have a tale, he is one of the most favorably described characters:

He was an honest worker, good and true,
Living in peace and perfect charity,
And, as the Gospel bade, so did he,
Loving God best with all his heart and mind
And then his neighbor as himself.

Perhaps the Plowman is too good to have an interesting tale. Most of Chaucer's pilgrims tell tales that reflect in some way on their own imperfections or obsessions, but the Plowman doesn't appear to have any of those. He has a brother who is also travelling with the pilgrims, the Parson, who is also an upstanding character, and the only member of the clergy Chaucer does not depict as corrupt in some way.