No. The Giants have the most players enshrined that have one teams logo (23) and who have played for them (66). While the Yankees only have 21 in as a Yankee, and 52 as a whole.
The Baseball Hall of Fame have 297 individuals to be inducted (236 players, 20 managers, 9 umpires, 32 pioneers/executives), the inductees that've been on the Yankees at some point are:
Frank Baker (A's)
Yogi Berra (Yankees)
Wade Boggs (Red Sox)
Jack Chesbro (Yankees)
Frank Chance (Cubs)
Earle Combs (Yankees)
Stan Coveleski (Indians)
Joe DiMaggio (Yankees)
Bill Dickey (Yankees)
Leo Durocher (Dodgers)
Whitey Ford (Yankees)
Lou Gehrig (Yankees)
Lefty Gomez (Yankees)
Joe Gordon (Yankees)
Goose Gossage (Yankees)
Clark Griffith (none) exec
Burleigh Grimes (Dodgers)
Bucky Harris (Senators)
Rickey Henderson (A's)
Waite Hoyt (Yankees)
Miller Huggins (Yankees)
Catfish Hunter (none) couldn't decide between A's or Yankees
Reggie Jackson (Yankees)
Willie Keeler (Highlanders (later became Yankees))
Tony Lazzeri (Yankees)
Bob Lemon (Indians)
Mickey Mantle (Yankees)
Bill McKechnie (Reds)
Joe McCarthy (Yankees)
Joe McGinnity (Giants)
John McGraw (Giants)
Johnny Mize (Cardinals)
Phil Niekro (Braves)
Herb Pennock (Yankees)
Gaylord Perry (Giants)
Branch Rickey (none) exec
Phil Rizzuto (Yankees)
Wilbert Robinson (Dodgers)
Red Ruffing (Yankees)
Babe Ruth (Yankees)
Joe Sewell (Indians)
Enos Slaughter (Cardinals)
Casey Stengel (Yankees)
Dazzy Vance (Dodgers)
Paul Waner (Pirates)
Dave Winfield (Padres)
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16 Hall of Famers
12 Hall of Famers were Boston Red Sox
500
Hall of Famers before the 1930s weren't since there was no all-star game then. I am not sure about ones after that.
Fourteen