Yes, it is very important.
While McCarthy will be heavily involved in implementing his playbook and coaching the finer points, the OC will be the one doing the heavy lifting. They will do the majority of the game prep and scheme to attack this week's opponent. McCarthy will have input in it as well, probably signoff more than anything. He will then call the plays during the game.
This is no different than Andy Reid does in KC, Doug Pedersen does in Jacksonville, and Mike McDaniel does in Miami.
It is the way it should always have been. It was the dumbest move in the world to hire an offensive mind, who won a super bowl with his offense and calling plays....to neuter him from having really any input in the offensive scheme. I wasn't a fan of hiring McCarthy in the first place, but if I did, I would absolutely let him bring his offense with him.
That was another mistake the Jones' have made. People don't talk about this at all.