Two things stand out about this Tale. The first is the the Second Nun references an earlier work by Chaucer, The Legend of Good Women, which was written as a serious book of instruction and edification, not as a humorous nor a tragical dream vision.
The "Second Nun's Tale" is a serious one. While Cecelia is not named in Good Women, the nun's tale about her, which she claims was translated from Good Women, must be taken in the same spirit as that which Chaucer admonishes in the Prologue to Good Women, as excerpt from which follows that gives the reason for reading, believing and keeping old books and tales:
Then in all reason must we give credence to these books, through which ancient things are kept in mind, ... And if old books were all gone, then the key of remembrance would be lost. Well ought we then to believe old books, where there is no other test by experience. (Chaucer, The Legend of Good Women)
The second thing that stands out, which is commented upon by scholars, is that there are no jaunty conversations or comments that preceed or follow the Tale: no one takes a rowdy or jocular attitutde toward the Second Nun's tale.
In light of the seriousness of the Tale, it is difficult to think that Chaucer would also impose a parody within its text. it is possible that with the jaundiced eyes of our own era, we might read (rather misread) the Tale or portions of the Tale and thereby "discover" a parody within.
That said, one view might be taken that recognizes Cecelia's marraige whilst celibate to a man who agrees to celebacy as a parody upon extreme relgious devoutness or upon the ineptitude of nuns and Pope Urban. Given the above and given that such female chastity was a respected religious option at the time Chaucer wrote, it might be difficult to defend this as a parody unless it is framed as a view from our perspective.
That on the day of marriage she was clad
(Beneath her golden robe so lovely) in
A shirt of haircloth right next to her skin.
And while the organs played, her heart inside
To God above was singing silently: 135
"Lord, to my soul and body too be guide,
Keep me unstained, lest I confounded be."
For love of him who died upon a tree,
Each second day and third she spent in fast,
Each day in fervent prayer from first to last. 140
Then came the wedding night, when to the bed
With her new husband she would have to go;
And privately at once to him she said,
"Sweet husband whom I love, and dearly so,
There is a secret I would have you know,