Yes, I would interline them. The faux silk is not that heavy and so it would add a nice weight to them so they drape well. If these are pull drapes, interlining will help insulate from the heat and cold.
With real silk you have to interline them to protect them from the sun.

Yes interline them. The interlining makes the drapes have shape and they will drape much nicer. Silk is so thin it tends to just want to hang there, the interlining gives it some body.

If you go into any drapery shop they should have sample showing drapes with interlining and those without. I think it gives them a much more custom look and feel.

Many curtain experts recommend a light "baby" flannel as the lining for silk or faux silk curtains, and recommend interlining as well.

lch in addition to giving the drapery a nicer hang/balance/weight - depending on the interlining it can offer an insulation - if you use them to keep heat out in the summer or keep drafts out in colder weather - thermalsuede would work for that application