Well, I am loosly affiliated with them...more of an informal online thing. I dropped Grant a note to find out, from the horses mouth, so to speak. He could reply on this thread, so be alert.
For myself, I have cleaned the older G5 (spinnaker cloth) with Down Wash. After removing the foam, I simply dropped it in the washing machine on gentle cycle. It came out far cleaner than it went in. BTW, Down Wash works well on merino wool items. I have also used it on silnylon tarps prior to re-sealing them with no problems, though it does not remove actual stains (not quite true, but close enough.)
The Dyneema X cloth used by Gossamer Gear (GG) is good stuff. Being highly water resistant (water proof) it will likely not pick up stains. Most stains require a water media to facilitate the loose bonding that occurs in a stain...about the same as dying. With some detergent, it is possible to wash a pack and then actually dye it, since nylon usually picks up the water, hence the dye. But be aware that colors will NOT be true. Most dyes rely on a mixture and type of bond to give color. This may be lost with some dyes...black dye will dye blue, for instance. It will not pick up the brown component. Copper ions are generally bluish green. And, only some of the nylon material will absorb it...it is generally similar to a long thread with only the ends being dyed. Soo, a lighter dyed result is always expected. There is just not enough bonding sites for strong dyes. Factory pigments are usually mixed into the nylon. A dye or stain is more of a surface thing.
The foam in the shoulder pads/hip pads does not absorb large amounts of water, either. On gentle, I doubt that any signifacant residue would remain. But use caution with any detergents. I would use a softer soap, like Down Wash, to avoid issues with residues and possible alergic reactions while hiking. But, this may be just overkill. Neither the material, nor the foam shoulder pads absorb any significant amount. So, while not removable, I would guess that the shoulder harness would be OK. Again, you might not remove any stains, though, don't expect to.