Did Lieutenant Colonel Daniel Davis attain the rank General? Short answer: Yes.*
John Atchison, first major, vice J. Smith, resigned; James Ganson, second do, vice John Atchison, promoted.
Richard Waite, captain, vice James Ganson, do; Russell Davis, lieutenant, vice Richard Waite, do; Jacob Widener, lieutenant; Noble B. Douglass, ensign.
Frederick Roe, captain, vice Jones, deceased; William Henshaw, lieutenant, vice Frederick Roe, promoted; Matthew Dimie, ensign, vice William Henshaw, promoted.
Here's a document from the Pension Application of GENERAL Daniel Davis's widow (who later moved to Ypsilanti, Michigan):
General Davis was killed on 17 September 1814.
*Daniel Davis [Lt. Col. Ny Vols] in the Registers of Enlistments in the United States Army, 1798-1914 [NARA]:
"...Present at Plattsburgh as Col. ...Reported on Returns of Militia of State of N.Y. dated 1814, as Gen'l (Brigadier). Killed Sept. 17/14, at Ft. Erie, U.C."