Does he put in the same mediocre performance he does with the Canucks? If I'm not mistaken, the Rangers signed LaFontaine to make up for Messier's departure, and he put up a pretty similar performance to Messier, so I don't think it would have changed much. And it most likely wouldn't have stopped the Rangers from overspending for mediocre, ill-fitted free agents and missing the playoffs for several years.
The more interesting question probably is how would it have affected the Canucks. While many Nuck fans like to rag on him, without him, they probably wouldn't have hired Keenan, and the two of them are partially credited for helping Naslund become a great player. As well, Linden probably wouldn't have been traded, getting Bertuzzi, helping form a great duo for a couple years. No Bertuzzi also means no Moore incident. And later on, no Luongo. Perhaps without the seemingly toxic culture that Messier and Keenan brought with them,or perhaps with his 6 mil salary better spent elsewhere, the team doesn't finish in the basement in '99, bringing in the Sedin twins. There's just a lot of what ifs there.