I would test the fabrics you have. For each colored fabric you have, drop a small swatch into a glass of water along with a small swatch of the Kona white. Leave alone for about 24 hours. Look closely to see if any dye has leaked into the water. Swish the fabrics around in the water and leave alone for another 24 hours. Check and see if the white has picked up any colors. Some whites will pick up loose color and some won't.
Another way to test would be to machine sew a swatch of each batik fabric to a swatch of white fabric, then wash as you intend to wash your quilt. Observe whether the white picks up color from the batik.
At this point, I probably wouldn't prewash anything. If there is a batik that runs a lot in the test, then I might omit it or prewash just that one fabric. I wouldn't prewash an already appliqued block because the fabric could shrink and distort. Once the layers are quilted, the batting controls shrinkage and will not allow a block to distort the way an unquilted block can. If you feel an absolute need to prewash your already-made blocks, do it by hand and use Sharon Schamber's technique to "block" the blocks to correct size while still damp. (She has videos on Youtube.)
When the quilt is finished, the first washing is critical. At the very least, it needs to be done with a ***lot*** of water so that any dye bleeds become very diluted. Synthrapol in this wash is very helpful, but it requires hot water to be fully effective. If you do not want to use hot water, Synthrapol won't hurt but it also won't provide a lot of extra insurance that no dye bleeds will be picked up by fabrics.