The problem with the WWE Hall of Fame is that it's just that, a WWE Hall of Fame or to be exact, a Vince McMahon Wrestling Hall of Fame. It's not an actual wrestling hall of fame or else there would be much different guys in there then currently are. You'd have Bruno and Macho Man and Million Dollar Man instead of Koko B Ware.
With that said, like others said, if TNA becomes a legitimate rival to WWE in terms of buyrates and stays that way, Vince will never let Sting set foot in that Hall of Fame. However, if TNA fails and becomes, like KB said, just another trophy on Vince's bookshelf, I'm also not certain Sting will set foot in it basely solely on his own refusal to. This very topic comes up at every HOF and everyone's response deals with whether or not Vince will let him in. Sting did not want to be a part of the company after the takeover, I'm not certain he'll want to be a part of its Hall of Fame. After all, like I said, it's WWE's and Vince's hall of fame, not a wrestling one. The only way I can definitively say he will is if he has one run in WWE