After some interesting discussion regarding Horry's merits to be included in the Hall of Fame I decided to do a little digging. In the process I found evidence both for and against Horry being inducted to the Hall of Fame. Im sorry for bringing stats and facts to the discussion, I know they are not always welcome here : )
The following table was borrowed and adapted from Wikipedia. Some of the names in the list are immediately recognized while others not so much. Out of these players only Tom Sanders and Jim Loscutoff are not in the Hall of Fame. Out of these guys K.C. Jones, Sanders, Loscutoff and Ramsey can probably be considered role players. Role players in the HOF include KC Jones and Ramsey.
The career of KC Jones has been used before to argue for the induction of Horry to the HOF. It is my understanding that Jones was a defensive specialist (and therefore a role player?). The difference with him though is that he had a successful coaching career.
Another player that Horry might be compared to is Ramsey. Ramsey's numbers are better than Horry's but I dont know exactly why he was inducted. They are obviously not amazing numbers. He is considereted by some to be the first "sixth man".
I think this numbers show that it is not unthinkable for Horry to make it to the HOF. If defensive specialist can be inducted, why not fourth quarter specialists? Or winning championships specialists? On the other hand Sanders and Loscutoff have similar or slightly better career numbers than Horry and similar amount of rings and are not inducted in the HOF, providing a precedent for Horry to be left out.
Career stats for some of these players via www.basketball-reference.com: