Papi in the Hall will be fascinating. There is the PED smell around him if the writers want ... they did it with Bagwell, who is a much better player. That will make things complicated. Also, his value is entirely on offense - pure DH's have not had a lot of luck. To wit, comparing him with another great pure DH/non hall of famer:
Edgar Martinez: 65.6 fWAR in 2055 plate appearances, 30.7 fWAR in his 5 best seasons. 309 HRs, 1261 RBIs, .405 wOBA, .312/.418/.515
David Ortiz: 42.2 fWAR in 2072 plate appearances, 24.4 fWAR in his 5 best seasons. 456 HRs, 1506 RBIs, .390 wOBA, .285/.379/.546
Edgar is an unambiguously better player than Ortiz, and he fell to 25.2% in his 5th year on the ballot. In short, Papi's case is very tough to argue - although the large market and the spectacular TV highlights will help him.