I have dyed silk fabric, yarn & fiber, but not dupioni.
I agree with the concern about the thread being a different fiber. I'd also be concerned about the beads.
You are going to have to wash your fabric before you dye it so the dye takes evenly. That will change the hand of the fabric a lot. Silk can be dyed with acid dyes or fiber reactive dyes. If the thread is rayon, fiber reactive dyes will dye both the silk & the thread. If it's polyester it might stain a bit, but not be dyed. For dyeing silk I prefer acid dyes.
If you decide to proceed, cut a small piece of the fabric & test it using the process you will use for the final fabric. The amount of dye it takes to get the color you want varies with the amount of fabric.