I want to say if it is a stock stereo - yes. I changed out my stock stereo in my 2006 duramax and since I wanted to keep the steering wheel controls had to buy an adaptor. That adaptor had the chime in it. I had to return the adaptor twice because it wasn't loud enough - first two I could barely hear over the engine and couldn't hear as I drove down the road (got close to empty on fuel once because I didn't hear the chime). I doubt they changed them for 2008 and I would say you could remove the speaker wire to verify. I think I remember others on dieselplace.com saying they had to replace that speaker before.
2014 Jayco Jayflight 32BHDS
2015 Ford F250 Lariat 4x4 Crew Cab 6.7L Powerstroke