When I look at Galchenyuk's strenghts: shooting, puck handling and passing, I see nothing that makes me believe he can use these tools better at center than wing (or vice versa for that matter). Many east/west type wingers use these tools to create chances from anywhere once they cross the blue line. The last few games show this. If he can play like this over a full season he'll get excellent point totals.
As for stats, since two years ago when he fined tuned his shot (his greatest strength now), I bet there's not much difference when you somehow factor in health, quality of teammates, usage etc. For example, playing heavily sheltered minutes with Pacioretty and Radulov is not the same as playing less sheltered minutes with De La Rose and Lehkonen.
There is more to the game then point totals. Peak Desharnais had some excellent point streaks, yet we all know it was a bad idea to use him as a top 2 center, especially in the playoffs, due to his own massive flaws.
When I look at good teams around the league for the past few years, I don't see any that use a player with poor skating/hockey IQ as their top 2 center. The reason is simple. Centers need to cover more surface area and the surface area they cover is more critical. To cover adequately more surface area it's better if you're a good skater and/or if you are good at reading the play; the objective being to be in the right position. Galchenyuk scores poorly in those facets of the game, unfortunately. I wish he didn't because it would solve a big problem with the team but he is what he is.
Finally, yes, the Habs offense is not good as it is and clearly needs an upgrade.