I don't think he will be in the same conversation with McDavid when its all said and done. I think he will be more of a Sid Crosby or Teemu Selanne, which makes him better than just "best player in the current NHL." McDavid is going to break every record when he's done, and will be top 5 all-time, imo. But who knows, Bedard might grow 4 inches and put on 30 lbs and turn into a unicorn!!
IDK, I think he has a decent shot at getting up there in that convo. I know the situations aren't the same, but McDavid played in 45 games his rookie season and had a stat line of 16G/32A/48P. Bedard currently has 12G/12A/24P thru 28 games. He's not quite at the PPG+ level that McDavid was, and McDavid was injured his rookie season, but Bedard's shot is just soooo sweet. He can maneuver the ice similar to McDavid, not as fast or big, but he's such a natural goal scorer...more of a shoot-first player as McDavid has always had almost twice as many assists as goals scored.
EDIT: Though now that you mention it, I guess this description does match Crosby more than McJesus, so you're probably right about Connor vs Connor.
If the Blackhawks can keep surrounding him with solid young talent, he could be a perennial Hart Trophy contender. I don't think he'll lead the league in scoring his sophomore season, but he'll lead the league one day.
Either way, it will be interesting to see him come up behind McDavid (get your mind out of the gutter!) and hopefully we'll see more Connor-verse matchups in the playoffs.
Sidenote, I'm not a hockey historian, but what was it about the late 80s/early 90s that allowed such huge points numbers from players? Gretzky broke 200pts 4 or 5 times, Lemieux averaged 2pts per game...just insane numbers. Gretzky had a season where he scored 255 points for crying out loud...that is insanity. He had 100 points in 34 games. Think about that, in 3 more games than the lightning have currently played, he had DOUBLE the number of points Kucherov has. I wish I was old enough to watch hockey then. I can't imagine what watching Gretzky and Lemieux would have been like.