From Doc and DA's quotes, they plan on giving the veterans as much rest as possible. If the second unit can hold and even extend leads, the rest of the team will get more than enough minutes. The C's bench did a terrible job of holding leads last year... terrible (especially large ones). If that trend stops, players will get their minutes; if it doesn't, the starters will take up the minutes they've taken up in the past.
The depth has its advantages: limit veteran minutes (limiting wear and tear) in a season long preparation for another strong playoff run and having been plagued by injuries for the last 4 years... this gives us more than serviceable backups.
If anyone can manage player minutes, distribute accordingly, and not have the bench complain or sulk, it's Doc. If Popovich and the Spurs can do it, why can't Doc and the C's? Barring injury, it'll all come down to the second unit's ability to hold and extend leads.