I think it's more likely that Quirrell has the Resurrection Stone. When Harry shows him the Deathly Hallows symbol, he cuts their meeting short and hurries off somewhere. In canon, the stone was set into the Gaunt family ring, which Quirrell would have seen and would know the location of (it is implied that HPMOR follows the canon relationship between Tom Riddle and his family: "I have long since resolved my parental issues to my own satisfaction", "my family are long since dead at the Dark Lord's hand", Snape and Moody meeting at Tom Riddle Senior's grave).