No, and I think people are reading too much of what Drew said.
He is competitor and a team player. He wants to leave with a trophy on hand. That is why he has no problem using Taysom more. But that doesn't mean he is ready to stop being the starter.
Many times it has been written that the way Drew (and most start quarterbacks) teach their proteges is by example.Drew won't take time of his schedule to teach Teddy and Taysom, but he will include them in his process and give them pointers.
Now, about sharing quarterback responsibilities, what Drew is saying is that he won't be opposing on using Taysom IF that is needed to earn more wins. What he means is that he is willing to give Taysom more plays by design, or when needed if the offense is not working.
But let's be clear: Neither Drew nor Sean Payton will use the 2020 season for preparing for the future. They won't be giving drives to Taysom or Teddy in order to have a more prepared quarterback of the future.
They will be riding Drew as much as they can, because that is what they think is the best option to go all the way.
It's just common sense, not much to read about this.