NO!
items shrink in a washing machine for 2 reasons. One is temperature, so wash them on 30 or below.
but the other is the agitation of the machine which encourages the weave of the fabric to sort of move closer together. And extreme version of this is the wool jumper that turns to felt in a washing machine.
So the wool cycle relies on the fabric soaking in water, with very little movement except the spin.
Dry cleaning won't necessarily get the dirt out anyway. It disolves some things, but not others and general grime, like when you live near a main road, rarely comes out with dry cleaning.
I used to work in a dry cleaners and laundry.
Honestly it is a gamble. There is a risk that they will shrink, and that the lining will shrink more/less.
Clothes fabrics are usually pre-shrunk, but not curtain fabrics, and they may well shrink (if you ever make your own, pre-wash the fabric before making the curtains)
But if they don't shrink, or so little that it doesn't matter, then washing will make them much cleaner than dry cleaning
30 degrees or lower, wool cycle.