A:
Hi Nanette,
UV protection is inherently higher in some fabrics; polyester has a very high UV rating because of the way the molecules reflect light. The added UV protection in your garment is most likely due to a special dye in the fabric and special laundry additives. The special dye will not wash away or be affected by embroidery or silkscreening. Laundry additives may wash out eventually after enough cleanings, but this still does not affect embroidery or silkscreening.
So the answer is no, embroidery or silkscreening will not diminish your UV protection. In fact, it will increase UV protection in the immediate area of the patch.