Mary's ancestry has not been found to my knowledge.  It is likely they were married in England before coming to America. However, it is also possible Mary and James married after coming, especially if James came as an apprentice to John Brown as is speculated.
A search of families surrounding the Phips' home site near Woolwich may yield Mary's ancestry as it was common for neighbors and families to migrate in groups.  Search the families of Hayward, Hammond, Cole and Brown to start with.

MARY was born  in England2, and died Aft. February 19, 1703/04 in Maine3.  She married (1) JAMES PHIPPS Bef. 1636 in Bristol, England4, son of WILLIAM PHIPPS and ELIZABETH.  She married (2) JOHN WHITE5 Bef. 1661 in Kennebec township, Maine6, son of NICHOLAS WHITE and DEBORAH FORD.   5 - 8 more children by 2nd marriage?  On October 04, 1679, she and husband White deeded Jeremisquam Neck, Maine to Sir William Phipps7
Sir Wm. Phipps' legatee, Mary, claimed the tract--"Cherysequamy Neck (sp)"--"as by deed from John White and Mary, his wife, formerly the wife of James Phipps of Kennebeck deceased; dated Oct. 4, 1679." [Me. H. and G. Reg. VIII, 202.]
She married (3) HOWARD - wish I knew who he was!
On February 19, 1703/04, her daughter in law Mary Sargent (Mary Spencer Hull Phipps Sargent) willed her 10# annuity8

Reverend Cotton Mather began the tale of Mary and James Phips' family of 26 children when he wrote Pietas in Patrium: Life of His Excellency Sir William Phips, Knt. in 1697.  The tale perpetuates to this day. Although there were large families known of in New England during those years, it is highly unlikely that one woman produced 26 children in one marriage, and then another 5-8 children in a second marriage!
Especially given the fact that of the supposed 26 children of James and Mary, only 6 children have ever been named.  Also consider that if James Phips was born between 1606-1612, and married at the age of 22 (an average marriageable age for a man in that day), the marriage of James and Mary would have taken place between 1628 and 1634.  James was dead by 1654, leaving 20-26 years in which he could have fathered the 26 children!  Unless there were several multiple births it is clearly impossible given the time factor alone.
I would like to submit that it could have been possible for Mary to have parented 26 children - but not 26 biological children. It is possible that of her 3 marriages there were 26 natural and step children, making her 'mother' to all.