Is the correct pronunciation of "Have you seen Mary's book" "Mary book"?

One American dialect where you can say Mary book rather than Mary's book, is African American Vernacular English, spoken mainly in the African American community. See this article.

An excerpt:

Possession in AAVE is also different. It can be shown by proximity where the owner’s name comes before the object owned. For instance, “She over Mary house” (Dandy, 1991, p.49). In this sentence you know that the house belongs to Mary because her name precedes the object owned. However, in SE, the only way to show possession is to add 's after the owner’s name.

In all other dialects of American English I am aware of, including standard American English, you need to pronounce the /z/ in Mary's book (although not always in other possessive phrases, like Claude's stuff or James's coat).

The omission of the possessive suffix is very common in many Caribbean dialects. Here's a short excerpt from an article on Trinidadian folk speech that happens to include your "Mary book" example:

With regard to expressing the possessive concept, inflectional suffixation is completely lost in the folk speech. Standard English marks possession in nouns by inflection and word order. To the noun is added the inflectional morpheme {s}, and the inflected noun is placed before another noun and its modifier or in the final position after a copula: Carl's pencil; the pencil is Carl's. Trinidadian folk speech dispenses with suffixation altogether when showing possession but follows the adjective word order: Carl pencil, Mary book, and so on.

Henry Richards (1970) Trinidadian Folk Usage and Standard English: A Contrastive Study, Word, 26:1, 79-87, DOI: 10.1080/00437956.1970.11435582

This is called a zero possessive and it is fairly strongly argued by some linguists that it is not (as others have it) "lazy", merely dialectal, or indeed even incorrect. Rather, it is the correct grammar of creoles such as Trinidadian Creole; and a form, moreover, that is considered the origin of the same construct in AAVE and what has been termed Black British English or Black English Vernacular.

Here is William Alexander Stewart on the subject:

For the teacher, this means that such "Negro" patterns as the "zero copula", the "zero possessive" or "undifferentiated pronouns" should not be ascribed to greater carelessness, laziness, or stupidity on the part of Negroes, but rather should be treated as what they really are — language patterns which have been in existence for generations and which their present users have acquired, from parent and peer, through a perfectly normal kind of language-learning process.^{Stewart 1968}

John H. McWhorter asserts that this is the sort of grammatical simplification that can be seen throughout the centuries through Old English and Modern Standard English through to Black British English and such creoles. He also makes the point that it cannot be traced to influence from British English dialects or to West African languages, none of which exhibit this feature to anywhere near an equivalent degree. ^{McWhorter 2008 p. 58}

Luisanna Fodde says that the zero possessive and other such grammatical features —

— have a very high sistematicity and precision of expression. They are never careless omissions or a proof of linguistic confusions.^{Fodde 2003 p. 494}

William Labov argues that treating the zero possessive as the elimination of consonant clusters, as the quotation in the question does, is "not the most likely interpretation" given that it "is absent after vowels just as frequently as after consonants for many speakers" of Black British English.^{Labov 1972 p. 24}

• William A. Stewart (Spring 1968). "Continuity and change in American Negro dialects". In Alfred C. Aarons The Florida FL Reporter. Volume 6. Issue 1. pp. 3,4,14–16,18.
• John H. McWhorter (2018). "Is Creolization just Language Mixture?". The Creole Debate. Cambridge University Press. ISBN 9781108428644.
• Luisanna Fodde (2003). "Ethnic dialects and mainstream English in the U.S.A.". In Carmela Nocera, Gemma Persico, Rosario Portale Rites of Passage: Rational/Irrational Natural/Supernatural Local/Global. Rubbettino Editore. ISBN 9788849806571.
• William Labov (1972). "The Structure of BEV". Language in the Inner City: Studies in the Black English Vernacular. University of Pennsylvania Press. ISBN 9780812210514.