The earlier statement about Pearson/Harris is not true. They are the only position players on the 1970's All Decade First team to not be in. There are others on the Second Team that didn't get selected for the HOF as well.
Here's the non Hall of Famers for all of the All Decade Teams (keep in mind that the All Decade Teams for the 1920s through the 1960's were selected in 1969 in honor of the NFL's 50th season)
COWBOYS AFFILIATION IN BOLD:
1920's All Decade Team - E Lavern Dilweg, G Hunk Anderson (also coached the Bears and Notre Dame)
1930's All Decade Team - QB Cecil Isbell, HB Beattie Feathers (1st player in league history to rush for 1000 yards), E Gaynell Tinsley, T Frank Cope, T George Christensen, T Bill Lee, G Ox Emerson, G Buckets Goldenberg, G Russ Letlow, G George Svendsen
1940's All Decade Team - HB Byron "Whizzer" White, FB Pat Harder, FB Bill Osmanski, E Jim Benton, E Jack Ferrante, E Ken Kavanaugh, E Mac Speedie, E Ed Sprinkle, T Al Blozis,
T Bucko Kilroy (a great player who made huge contributions as a scout, was a Cowboys scout), T Buford Ray, T Vic Wears, T Al Wistert, G Bruno Banducci, G Bill Edwards, G Buster Ramsey, G Len Younce, C Charley Brock
1950's All Decade Team - FB Alan Ameche, E Bobby Watson, G Dick Barwegan, G Dick Stanfel, LB Joe Fortunato
1960's All Decade Team - HB John David Crow, SE Del Shofner, FL Gary Collins, FL Boyd Dowler,
OT Ralph Neely, OG Howard Mudd (all time great OL coach as well), OG Jerry Kramer, DT Alex Karras, LB Larry Morris, LB Tommy Nobis, CB Bobby Boyd, S Eddie Meador, PK Jim Bakken, P Don Chandler
1970's All Decade Team:
First Team: WR Drew Pearson, S Cliff Harris, PK Garo Yepremian, KR Rick Upchurch
Second Team: QB Ken Stabler, WR Harold Carmichael, DE L.C. Greenwood, S Dick Anderson, PK Jim Bakken, P Jerrel Wilson, KR Billy 'White Shoes" Johnson
1980's All Decade Team:
First Team: OT Jimbo Covert, S Kenny Easley, PK Morten Andersen, P Sean Landeta, KR Mike Nelms, PR Billy "White Shoes" Johnson
Second Team: FB Roger Craig, OT Joe Jacoby, OG Bill Fralic, DT Keith Millard, DT Dave Butz, LB Carl Banks, LB John Anderson, CB Frank Minnifield, CB Lester Hayes, S Deron Cherry, S Joey Browner, S Nolan Cromwell, PK Gary Anderson, PK Eddie Murray, P Reggie Roby, KR Rick Upchurch, PR John Taylor
1990's All Decade Team:
First Team: OT Tony Boselli, LB Kevin Greene, S Steve Atwater, S LeRoy Butler, PK Morten Andersen, P Darren Bennett, KR Michael Bates
Second Team: QB Brett Favre, RB Terrell Davis, TE Ben Coates, OT Richmond Webb, OG Steve Wisniewski, C Mark Stepnoski, DE Neil Smith. DT Bryant Young, LB Hardy Nickerson, LB Cornelius Bennett, LB Levon Kirkland, S Carnell Lake, PK Gary Anderson, P Sean Landeta, PR/KR Mel Gray
The team for the 2000's has far too many eligible, active and non-HOF players to list.