This is what I have on that family (please note: Most of this is NOT my own research, but culled from online trees, other people emailing me, etc. - take this as a HINT to follow up on, not gospel).
This part we DO know:
William Drew, b. 1763 Redding, Fairfield Co., Ct. d. Dec. 25 1836 in New Baltimore, Green Co., NY (bd. in Palmer Cemetery, New Baltimore). He was the son of William Drew of Ct., b. 1746, possibly the son of John Drew b. 1724, of Redding, Ct.) wife: unknown

William Jr. He filed a petition for a Rev. War pension while living in Green Co.
Summation of that application:
Rev. War: he filed a petition, signed Feb. 9, 1836 in Greene County, NY indicating:
born in Redding, Fairfield Co., Ct. in 1763; entered into service in Manchester, Vt., in 1778, in the infantry under Capt. Gideon Bronson; regiment of Col. Ethan Allen; worked in a blacksmith shop which Col. Allen's father owned (worked there through Rev.); then moved to 1786 to Peekskill Center;
On list of "American Revolutionary War Rejected Pensions" - William Drew, New Baltimore, Greene, NY "he was a blacksmith - name not on the rolls". (His brother Ezra's application was also rejected - he was also a blacksmith.)

Wm.'s movements per that petition:
Born in Redding, Ct.
1778 - Manchester, Vt. when he entered war; worked a blacksmith shop; father also an enlisted soldier in Manchester; cont. in Manchester after the war
1786 - removed to Peekskill, county of Dutchess
then to Albany
then to Kingston, Ulster Co.
then to New Baltimore, Green Co., NY

I did not find probate for him in online index for Greene - but it may be worth looking there anyway for some sort of filing and for deeds.

I have for William's ch: (this part is not proven, but assumed because they all lived together in close proximity in Greene Co.)
James b. 1797 md. Nancy b. 1813 Canada 1850 and 1860 in New Baltimore
Harriet b. abt. 1800 md. Hiram Fisk, Greene Co., NY
NANCY b. 1807, d. 1897 md. Copeland Palmer (1803-1870), bd. Medway Christian Cong. Church Cem., New Baltimore
William Henry b. 1816- d. after 1896 (he was living in the almshouse in Cairo, Greene Co. that year)
Schuyler, b. 1828 d. 1892, md. Charlotte, (both bd. in Medway Cem)

As to American Indian heritage in the Drew line, the southern Drews seem to have such connections, but not the New England Drews (as far as I know).

If you have any knowledge of a descendant of William Drew of Ct. (a male Drew), we would LOVE to have that person's DNA tested to see whether there is any (even remote) relationship to that line and ours (Gilbert Drew b. 1732).