Yes, you can embroider all three layers without any problem....however...... keep in mind that you may have some shifting of the layers because of all of the re-hooping AND your bobbin stitches will show on the back of the quilt. While that may be OK with redwork type designs, it won't look good if you use some of the designs that are a bit more complex.
My method is to embroider the blocks, then piece the quilt, then quilt as usual. Even if you just stitch in the stitch between your blocks to hold all of your layers together, you will have a prettier finished quilt.
Here's a link to an embroidered quilt on my site:
http://www.candyapplequilts.com/embr...-beauty-quilt/
This was embroidered first, then assembled, and then quilted. You can always do all of the basic quilting to stabilize your layers, and then keep adding to it (such as more stippling, etc.) as the spirit moves you.