Is it official Catholic dogma that Mary is the wife of the Holy Spirit? I've seen many posts here from Catholics describing Mary as the spouse or wife of the Holy Spirit. Catholic Answers calls it a "pious custom".

Is this official Catholic dogma? If so, when was it formally defined? If it isn't, then how widely supported is it? Where along the path to dogma described by this question is this belief?
It is not dogma

Were it a dogma you'd find a record of it at the Pope's official web site.  

Ludwig Ott states in his Fundamentals of Catholic Dogma that, 


  "The Church honours her on account of her position as Mother of God, and on account of her high endowment with grace deriving from her position as daughter of the Heavenly Father and Spouse of the Holy Ghost." (Part 3 {The Mother of the Redeemer}, Chapter 1, Section 2 (p. 196))   


Ott does not list it as a dogma of the church. (thank you, @zippy2006) (Nor does Denzinger clearly identify this pious belief as a dogma).   

The two dogmas most recently published, and in these two cases pronounced ex cathedra, concerning Mary are the Assumption and the Immaculate Conception.  We have Q&amp;A on both of those topics.  That they are both alluded to during Adoration seems to bear on your question.  Remember that the Church won't endorse polygamy.  During the holy hour of Adoration (which has seen a revival ever since John Paul II became pope), during the  Reposition the faithful pray The Divine Praises  


  Blessed be God. Blessed be his holy name.
  Blessed be Jesus Christ, true God and true man. Blessed be the name of Jesus. Blessed be his most Sacred Heart. Blessed be his most Precious Blood. Blessed be Jesus in the most holy sacrament of the altar. Blessed be the Holy Spirit, the Paraclete.
  Blessed be the great Mother of God, Mary most holy. Blessed be her holy and Immaculate Conception. Blessed be her glorious Assumption. Blessed be the name of Mary, virgin and Mother.
  Blessed be St. Joseph, her most chaste spouse.
  Blessed be God in his angels and in his saints. Amen.    


No pope has formally declared the Holy Spirit's "spouse" being Mary to be dogma (by speaking ex cathedra) nor condemned it.   (To answer your comment: why would they condemn such a belief?  See Ott's observation above).  Only the Pope can define or reject something binding on Catholic belief one way or another (dogma).  

The Catholic church embraces a variety of expressions of belief and faith (for example scapulars, and other sacramentals) without them becoming dogma.  Your look into this "pious custom" has already given you your answer at the Catholic Answers ... but do they have the Nihil Obstat?  (no).  If you check the Catholic Encyclopedia, its treatment of Mary does not include a discussion of her being the spouse of the Holy Spirit.  Nor do you find it as a dogma on the Pope's official site at vatican.va.  

The church does not go out of its way to keep a nearly infinite list of "Oh, and this isn't dogma, nor this, nor this ..." - it's rather pointless.     

No: the position or belief that Mary is the spouse of the Holy spirit is not dogma.  You are invited to read up on an official written discussion of dogma and its formation here.   

An excerpt of the much longer treatment ... 


  The study of the history of dogma shows clearly that in these dogmas the Church has not simply taken up already existing conceptual schemes. She has rather subjected existing concepts, imprinted by the upper levels of the language of the milieu, to a process of purification and transformation, or reworking. In that way, she has created the language that fits her message. Take for example the distinction between "substance" (or nature) and "hypostasis", and the working out of the concept of person which was unknown, as such, to Greek philosophy. In fact, it came about as a result of reflection on the reality of the mystery of Salvation and on biblical language.  
  
  The language of the Church's dogma was then forged partly in debate with certain philosophical systems, but is not bound in any way to any definitive philosophical system. In the process of seeking language for the faith, the Church has created a language of her own in which she has given expression to realities hitherto unperceived and unknown, but which belong now, precisely by means of such linguistic expression, to the Paradosis of the Church and through it to the historical heritage of humanity.