David Starkey's Six Wives: The Queens of Henry VIII contains some information pertinent to your question, and although the answer may not satisfy you, I believe it is the extent of current scholarship on the subject.

(Caveat: Starkey's work, which is aimed towards a broad popular audience, is not universally well regarded among historians. See the following review of the book for more information.)http://www.jstor.org/stable/20477541

To sum up, Starkey claims that there is no evidence that Holbein's portrait at all influenced Henry to marry Anne of Cleves. In particular, there is no historical evidence to the popular claim that Henry exclaimed on seeing Anne in person that she looked like a "Flanders mare."

By comparison, Holbein was also commissioned to create a portrait of Christina of Denmark (http://www.nationalgallery.org.uk/paintings/hans-holbein-the-younger-christina-of-denmark-duchess-of-milan) for the same purpose as the portrait of Anne, to help Henry choose a bride. Despite Christina's portrayal in somber mourning clothes in the painting, Starkey presents evidence that Henry was so enchanted by the portrait that he ordered musicians to play for many hours to create a mood of love, while he admired it in detail.

Henry being so drawn to Christina of Denmark's portrait but electing to marry Anne of Cleves suggests there were factors beyond Anne's beauty in Henry's decision to marry. Any thoughts on his immediate "buyer's remorse" would be speculation on my part.