The following players lasted more than one HOF ballot since 1990, despite dubious credentials:
Harvey Kuenn, 100 HOFM, 15 years, 14.6% - 39.3%
Roy Face, 47 HOFM, 15 years, 5.3% - 18.9%
Sparky Lyle, 65 HOFM, 4 years, 3.4% - 13.1%
Rusty Staub, 59 HOFM, 7 years, 3.8% - 7.9%
Dave Concepción, 106 HOFM, 15 years, 6.8% - 16.9%
Bob Boone, 102 HOFM, 5 years, 4.2% - 7.7% (perhaps the most-optimistic-case precedent for Varitek)
Dave Stewart, 75 HOFM, 2 years, 4.9% - 7.4%
Fernando Valenzuela, 66 HOFM, 2 years, 3.8% - 6.2%
Willie McGee, 84 HOFM, 2 years, 2.3% - 5.0%
Harold Baines, 66 HOFM, 5 years, 4.8% - 6.1%
(Varitek: 54 HOFM, 24.3 career bWAR)
One thing I noticed while going back 25 years of HOF voting is that the number of bad candidates kept alive has dramatically declined in the last 10-15 years. Basically nobody with a HOFM under 100 gets 5% these days. The biggest travesty (and perhaps the only one) since 2000 appears to be Bruce Sutter's election in 2006, and arguably Baines staying on from 2007-2011. So based on all that homework, I think I've got a worse side of this argument than I'd realized. Looks like odds of Varitek's survival, while not zero, are probably no more than 10%.