In case you don't want to read this whole long post, the short answer is no, quilter's temporary basting spray does not wash out. It will eventually stop being sticky, but I don't think it actually goes away when washed (at least the two brands I tried didn't wash out when washed in cold water).…
This is the #1 basting method for quilts. (Say GOODBYE to pins
Chainstitching on a Touch & Sew
How to Use Basting Spray with Cuddle®
June Tailor JT440 Quilt Basting Spray, 10 ounce can Vietnam
SK-100 Temporary Quilt Basting Embroidery Spray Adhesive for Fabric
Holding the Quilt Sandwich Together – Quilts, Quips, and other
505 Adhesive Spray – Quality Sewing & Vacuum
This is a clear, needle-friendly spray for fabric and crafts. It offers a temporary hold that will not gum sewing needles. This basting spray is repositionable with no residue. It is colorless and acid-free with no CFCs.
Pellon Spray-N-Tack
basting spray? : r/quilting
Stay Put Spray Adhesive Classic Styles
Temporary Adhesive 505 - Odif, Adhesive, Varnish and Color for
Does Temporary Basting Spray Wash Out?
SpraynBond Basting Adhesive is a temporary bond spray adhesive for fabric. Use it in your design phase for pattern piecing and determining appliqué
SpraynBond Basting Adhesive Fabric Spray
Spray Basting - Will it Work for Me? #2 - New Every Morning