As pointed out by Stratton in his book, the only complete list of Mayflower passengers, if it is complete, were from notes made by Gov. William Bradford over thirty years later. As he points out, the list has held up over the years. Our Henry Rowley was not among the passengers.
In 1623 there was a "Division of Land" among the residents of the Plymouth Colony. Each head of family received acreage based partially on the number of family members, including servants, as well as other factors. The 1623 Division of Land thus serves as a census of sorts of the colony, and again, Henry Rowley does not appear.
A list consisting of 53 Plymouth Colony residents and five London investors made up the 1626 agreement between the "Adventurers" and the "planters" of Plymouth. These fifty-three colonists were a privileged group and the list did not include all. But, it is another list to be searched. Henry was not there.
On the 22nd of May in 1627, the Plymouth Colony Court decided that the "Cowe, & the Goates" should be equally divided "to all psonts of the same company." It is believed that list includes the name of every resident then at Plymouth, including servants and children. Because of that, this is an important list of inclusion or exclusion. Henry Rowley is in the latter category (exclusion, that is). 
In the city of Scituate, Massachusetts in a graveyard named "Men of Kent Cemetery" there is the monument pictured above, perhaps ten feet tall, inscribed on the other side:
In Deane's history of Scituate,he states unequivocally, "It is certain that William Gillson, Anthony Annable, Thomas Bird, Nathaniel Tilden, Edward Foster, Henry Rowley, and some others were here before 1628." This is especially hard to refute since the Plymouth Colony deeds list a record where Henry Merritt of Scituate sold Nathaniel Tilden a piece of land in Scituate dated 10 April 1628.
However, that is just what has occurred. In the April-June 1994 issue of Great Migration Newsletter, They state, "In the first volume of Plymouth Colony deeds. . . is a record whereby Henry Merritt of Scituate sold to Nathaniel Tilden of the same town a parcel of land in Scituate, dated 10 April 1628, but recorded 20 April 1644. This is one of a series of deeds recorded the same day, all conveying Scituate land, the others being dated from 1636 to 1643. As there is no record of the parties involved in this deed being in New England before the mid-1630s, the date of this document should more likely be 1638, and the proposed settlement of Scituate by 1628 must be rejected."
As late as March, 1633 Timothy Hatherly was referred to in the Plymouth Colony Records as, "Tymothy Hatherly, mercht of London. On the first pages wherein the names of the freeman of the incorporation of Plymouth in 1633, the names of Thomas Bird, Henry Merritt, Nathaniel Tilden and Edward Foster do not appear(although Timothy Hatherly does appear under a listing "The rest admitted afterwards"-- as did Henry Rowley).
What is more telling, however, is the General Court's clues as to the founding of the community of Scituate. According to the Great Migration Newsletter, on 1 January 1633/34 three constables were appointed, one for Plymouth, one for a ward bounded between Jones River & Green's Harbour, and the third "for the ward of Scituate." The ward between Jones River & Green's Harbour became Duxbury.
The designation of the two areas as "wards" indicates they were not viewed as separate towns, but as outlying parts of Plymouth. The Great Migration researchers also found, by comparisons with later lists of town officers, the colony from the start maintained lists in the order in which the towns were founded: in 1636/7, there were Plymouth, Ducksbury and Scituate. In 1638/9 - Plymouth, Duxborrow, Scituate, Sandwich, Cohannet [Taunton], and Yarmouth.
The end result of this tale is: we don't know! He arrived in the colony after 1627 and by 1633. One theory that keeps popping up is that Henry Rowley was part of the congregation meeting in their private sanctuary, a room in the house of Mr. Humphrey Barnet, brewer's clerk in Black Friars in London. Bishop Laud's henchman, Tomlinson seized forty-two including Rev. John Lathrop on the 22nd day of April 1632. Eighteen escaped. To where? Possibly to the colonies. If Henry Rowley was one of them, it would account for the lack of records, because he certainly would have had to leave the country under the cloak of secrecy. Do not forget the words written by John Lathrop in Scituate after his arrival in the Plymouth Colony: "Upon January 8, 1634 (O.S.) Wee had a day of humiliation & and then att night joyned in covenaunt together. So many of us as had beene in Covenaunt before."
 Ibid, p. 415.
 Ibid, p. 419.
 Ibid, p. 421.
 Samuel Deane, History of Scituate, Massachusetts, From Its First Settlement to 1831. (Boston, Massachusetts: James Loring, Publisher, 1831), page 8.
 Nathaniel B. Shurtleff, ed., Records of the Colony of New Plymouth in New England, Volume XII, (Boston, Massachusetts, 1855-1861).
 Rev. E. B. Huntington, A.M., A Genealogical Memoir of the Lo-Lathrop Family in this Country, Embracing the Descendants as far as Known. (Ridgefield, Connecticut, Mrs. Julia M. Huntington, Publisher, 1884), pages 24-27.