I didn't see this mentioned... might have just missed it, but the only two 1st overall picks to not play immediately in the NHL in the last 20 years are Alex Ovechkin and Erik Johnson... and Ovechkin would have if there had been a 2004-05 season... so it's really just Johnson. And no one within the last 10 years. Even the lesser 1st overalls, like Hischier, play right away.
It's a perfectly reasonable assumption that he'll be on the team opening night... nothing about arrogance or laziness. Confidence, maybe... but nothing else.