I have several stamped cross stitched tablecloths handed down to me from my DH's grandmother and those blue markings fade a lot, but they have never come out entirely. Even the ones that have been laundered/cleaned many times, I can still see the faint blue marks. I suppose different manufacturers and different fabrics might give different results.
I see no reason why you can't quilt within the blocks in a few places for stability, as long as you don't stitch over the embroidery, as you said. This really will be a treasure when it's done, something you and your mom both put time and love into. I hope it winds up with someone very special.