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).…
SPRAYnBOND by HeatnBond Temporary Quilt Basting Spray - 158 g
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505 Temporary Fabric Adhesive 14.7oz Spray | Odif #43511
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Quilters' favorite basting spray: ODIF 505 Temporary Fabric Adhesive