Coffecozy:
Sagging will happen is there is no stitching to hold the batting and backing together. So, yes, the blocks need FMQ around the embroidery design or applique fabrics. Some of the designs have stippling already programed into the design steps. It is generally done after tack down of batting and background fabric.
If the design doesn't have the stippling, FMQ can be added. Some machines have stippling designs built into the machine. Easy to add to the applique design that doesn't have one.
Good luck!