It is conceivable that he could survive. He will be injured almost certainly no matter what. Other answers are correct that mail is not that good at dealing with piercing weapons. But it's not guaranteed to fail; it is possible for him to get lucky and have much of the shrapnel stopped by his mail. Especially if he isn't right next to the grenade when it goes off.
Further, any shrapnel that gets through the mail then also has to get through very thick padding. Nobody wore mail over bare skin, or even just light clothes. Whatever gets through both the mail and the padding then also must penetrate his flesh deep enough to cause a dangerous injury. Surface cuts and punctures will draw blood, but they won't take him out of the fight.
It's also conceivable that he could die. Shrapnel could go between the rings in his mail and puncture an organ. Or it could go in a gap somewhere, like the eye-slit of his helm. Or if he's very close to it he may suffer pulmonary edema from the pressure wave like Keltari said.
I think either outcome is believable, and you should decide which to go with based on what would be best for your plot.