They won't miss 2016 Diaw or West. They won't miss post AS break 2016 Duncan either.
Duncan will still be very involved and around the team to provide some leadership still.
Aldridge will be better and more comfortable in his 2nd year.
Gasol will be an improvement over the Duncan we saw last year when it mattered.
Dedmon will have a bigger impact on the ball movement and offense than West ever could last year-- mainly because the diving action with an effective roller opens up the weakside action so much more than the pick and pop action (I've elaborated so much on this on ST and twitter this summer). He'll also provide some solid interior D, more so than West ever could. Dedmons' skill set on both ends were needed desperately, and even though his stats won't be eye popping, his skill sets will make a very positive impact on the team -- a lot more than West did.
As of now, Anderson and Lee will compete for limited minutes at the PF. Anderson will also compete with Bertans and Simmons for minutes at the SF.
Gasol and Aldridge should see 60-65 minutes per game, more so than last years' starters in Duncan/Aldridge because Gasol is more capable of putting in more time on the court than 39 year old Duncan (Gasol played 32 mpg last yr). Dedmon should also see around 15-18 minutes per game, that leaves a little for Anderson and Lee to fight for. Sure there will be times when Gasol or Aldridge take a game off and rest, or there will be blowouts and Lee or Anderson should get more time in those scenarios. However, when it matters, I think you'll see Pop go to a three big rotation of Gasol, Aldridge and Dedmon with Kawhi getting some minutes at the PF if the situation calls for it.
Overall, the Spurs will be in much better shape in the front-court this upcoming season. This team will be better, maybe not from a win/loss perspective in the regular season but this upcoming group should have a much better end product once the playoffs roll around.