If Urban Meyer is telling the same story year in and year out about a turtle biting Woody Hayes in the dick as a sign of toughness, then one has to ask the hard questions, like, "Why did he tell the same story about Earle Bruce the year before?" (Go to the 10:00 mark or so.)
It is entirely possible that Urban Meyer simply has them confused. It is also possible that this is simply a very good story, and letting the truth get in the way of that story would be a crime. Coaches and snapping turtles in buckets have appeared in the same motivational story before: Mike Ditka allegedly did a similar trick, but wisely used his hand instead of his dick.
So let's examine the legend in particulate, and estimate the plausibility of each.
1. That a coach would use an animal in a motivational demonstration: plausible. If Jackie Sherrill would castrate a bull to prove a point, then we can certainly see either Earle Bruce or Woody Hayes grabbing a random turtle to prove a point. We could also see Woody Hayes eating the turtle for lunch and calling it "a feisty omelet," because Woody Hayes was documentedly insane.
2. That a coach would use his penis as a motivational tool: sadly, also plausible. If the President of the United States did it, then yes, the leader of a college football program would do it.
3. That a coach would allow a turtle to bite his penis: fairly plausible. There is no way of saying what a coach will and won't do. However, the Illinois coaching job never goes vacant, so it is entirely plausible that a coach would stick their dick in a snapping turtle's mouth.
4. That the turtle would not bite the penis off completely: plausible. Large snapping turtles like loggerheads can take off a finger. Those cases are rare, however, and require a very big turtle--certainly not the kind you'd tote around in a bucket or a shoebox. The penis is a durable piece of gristle, and with a small turtle would likely only suffer severe bruising and possible laceration.
5. That you could get it to let go: highly plausible. Just block the nostrils, dumbass.
6. That either Woody Hayes or Earle Bruce would do any of this: totally plausible. The most suspicious thing in the story is its similarity to the Ditka story and the confusion between the two Ohio State coaches. The least suspicious? That either of the two men involved would do it. Earle Bruce allegedly hit players with a closed fist on multiple occasions, while Woody Hayes hit an opposing player in the face on national television. Bruce and Hayes both had moments of total lunacy to make their participation here seem plausible.
IN SUMMARY: Some former Ohio State coach could very well have done this, and that coach was either Hayes or Bruce. A turtle could in theory bite a man in the dick without ripping it off, and then be removed with some ease. Urban Meyer could have seen this, and then relayed it with some faulty accuracy. The story does have some strong similarities to a previous story involving Mike Ditka. Oh, and Tim Tebow could have some real potential as a linebacker, JevanSnead. That's all Urban Meyer's saying
PLAUSIBILITY: Half-likely, and a push at best between reality and fabrication.