We cannot say this with any definitive proof, but we now have a tool by which we can make a pretty good guess, courtesy of David Pinto's wonderful Baseball Musings' Day By Day Database.

What this does is sort each team's players by team games won and lost while that player was in the game. The dataset used comes from Retrosheet, which means it goes back to the beginning of the 1957 season (that's as far back as Retrosheet has every single game so far), fifty years' worth.

I ran the data. Save yourself time, it takes a long time to load (and would take forever if you're on a dialup connection). All the results are here if you want to look, but here are some of the highlights:

• The "best" player over the last 50 seasons was Raul Gonzalez, who played in three games in 2000. The Cubs won all of them, no mean feat for that 97-loss club. I confess I have little memory of Raul.
• Only five other players over the last 50 seasons never played in a losing game in a Cub uniform, and there are a couple of interesting names here: Jim Woods (2 games), Jason Smith (2 games), Dave Dowling (one game, a two-run CG win as a pitcher), Tony LaRussa (yes, THAT LaRussa, one game, Opening Day 1973 -- he scored the winning run as a pinch runner, and it was the last ML game he ever played), and Adam Greenberg (you probably remember that one!).
• The player with the best winning percentage in Cub appearances after the six "undefeateds" is Randy Myers; the Cubs were 136-33 (.805) in his 169 games in a Cub uniform. Not surprisingly, many closers -- Lee Smith, Joe Borowski, Bruce Sutter, even Ryan Dempster (112-48, .700) appear near the top of the list.
• Great Cubs of the recent past: Don Kessinger, .488, Glenn Beckert, .488, Andre Dawson, .488, Ryne Sandberg, .483, Sammy Sosa, .480, Mark Grace, .479, Ron Santo, .478, Billy Williams, .471, Ernie Banks, .452. The only Cub of note who played in a significant number of games and finished over .500 (and that, just barely) was Randy Hundley (472-471, .501).
• 63 unfortunate ballplayers wore a Cub uniform over the last fifty seasons without ever appearing in a Cub victory. It'd be too time-consuming (and might freak you out too much) to name them all, but here are the bottom two: Wayne Schurr, a right-handed relief pitcher who threw in 26 games, all losses, in 1964; and Jack Warner, another righty reliever who pitched in parts of four seasons (1962, 1963, 1964 and 1965), appearing in 32 games without ever participating in a victory.