Absolutely, and in a perfect world the people who are doing the voting would be doing some thinking during that period. But I think that there's a significant percentage of voters who don't put any serious thought into a player's qualifications until he shows up on the ballot.
Here is a list of some pretty good players who received less than 5% of the vote in their first year on the ballot:
Bill Buckner (2.1 percent, 1996)
Ken Caminiti (0.4 percent, 2007)
Jose Canseco (1.1 percent, 2007)
Joe Carter (3.8 percent, 2004)
Norm Cash (1.6 percent, 1980)
Cesar Cedeno (0.5 percent, 1992)
Ron Cey (1.9 percent, 1993)
Will Clark (4.4 percent, 2006)
David Cone (3.9 percent, 2009
Cecil Cooper (0 percent, 1993)
Mike Cuellar (0 percent, 1983)
Darrell Evans (1.7 percent, 1995)
Tony Fernandez (0.7 percent, 2007)
Kirk Gibson (2.5 percent, 2001)
Dwight Gooden (3.3 percent, 2006)
Bobby Grich (2.6 percent, 1992)
Pedro Guerrero (1.3 percent, 1998)
Tom Henke (1.2 percent, 2001)
Frank Howard (1.4 percent, 1979)
Jimmy Key (0.6 percent , 2004)
Carney Lansford (0.6 percent, 1998)
Bill Madlock (4.5 percent, 1993)
Bobby Murcer (0.7 percent, 1989)
Milt Pappas (1.2 percent, 1979)
Boog Powell (1.3 percent, 1983)
Dan Quisenberry (3.8 percent, 1996)
Willie Randolph (1.1 percent, 1998)
Rick Reuschel (0.4 percent, 1997)
J.R. Richard (1.6 percent, 1986)
Bret Saberhagen (1.3 percent, 2007)
Ted Simmons (3.7 percent, 1994)
Dave Stieb (1.4 percent, 2004)
Dizzy Trout (0.5 percent, 1964)
Virgil Trucks (2 percent, 1964)
Bob Welch (0.2 percent, 2000)
Lou Whitaker (2.9 percent, 2001)
Frank White (3.8 percent, 1996)