I suspect you are not as familiar with Manx Records - remove any notions of the Lord Bishop sitting bewigged in a grand court house - the Episcopal Court which came under the Bishop's oversight was run by one of his vicars general - think of two clergymen - the Vicar General and his registrar sitting in a large room at a local inn (or possibly in the school or even church if nowhere else), on the previous Sunday the sumner would announce that a court was to be held and that those who wished to gain administration should make themselves known - legally administration could not be sought until a short time after death (to allow relatives to gather and locate any will) - if there was a verbal will then the witnesses had to contact a scribe (usually the local vicar) who wrote down their account and then they had to swear to this at the court which is whythey were always rewarded with 6d (the smallest denomination of silver - remember too that all documents had to be in English whereas most would have as first language Manx - hence the will would be translated by the scribe, a written will made and signed by the testator was a rarity. Some of the rules for running the court etc had been laid down by Bishop Barrow in his all too brief modernisation of the Chuch from the late 1660's. There would be 3 courts a year which circulated between the parishes 2 episcopal and one coming under the archdeacon but in all likelihood employing the same officers (the court fees merely finding their way to different pockets) - difficult (ie disputed) cases would be postponed to a later court for depositions to be made - in the more important of these the Bishop might sit as law officer.
Thus the court having a list of defuncts virtually rubber stamped the paper work unless there was a dispute by relatives - you can see this in that the court writes its acceptance + decision on the same paper which is then filed by the registrar - legacies still to be paid (sometimes years later) were acknowledged (crossing the books is a common phrase).

Now to return to Ann Corlet - the burial register for Ballaugh is lost for some 20 years from 1675 - as is also some years of the Marriage and Baptismal registers, thus you cannot know if Ann died as a child - all you have to go on is the appearance of a name in a will - thus a note of the baptism (and btw I have 1683 ) guarantees no proof that child survived nor who the mother was as before 1695 little additional information was given in the baptismal reg (my own impression is that the early reg is a copy) - you need to match with a will or other document - there are quite a number of wills pre 1690 that still await my attention - Ballaugh research is compounded by the Bishop's demense, the 16 or so tenant families could leave no land deeds (unless they also owned land outside of the demense) thus removing one of the mechanisms to trace families.

My own thoughts re Ann is that she married quite late to a widower with some young children - possibly she was a younger or the youngest dau of Wm Corlett who had landed up with looking after elderly parents - I can only match a few children (this is my interpretation - I'm afraid as I pointed out earlier matching on father's name alone is no guarantee that you have the correct family) which is consistent with age early 30's at marriage in early 1680's. The Margt Quiggin als Caine was the one married in 1708.