Bottom-line

“NO” and “YES”  Please see references below.

Discussion

What can be sewn on is referenced below:

DA PAM 670-1 Para 4-8e

Soldiers may sew on the U.S. Army tape, name tape, rank, and all authorized badges as an option. Hook-and-loop fasteners for U.S. Army tape and name tape may be left on or removed when sewing on the uniform. If worn, badges must be all sewn on or all pinned on; Soldiers are not authorized to mix sew-on badges with pin-on badges. When personnel sew on badges, the following must also be sewn on the combat uniform coat: name tape, U.S. Army tape, and grade insignia. If a nametape, U.S. Army tape or grade insignia is sewn on, then personnel must sew all three of these items on the uniform coat. This requirement does not apply to the patrol cap. If Soldiers choose to sew on U.S. Army name tape, rank or authorized skill badges, it will be at their own expense. Soldiers may wear pin-on badges with sewn on name tape, U.S. Army tape, and grade insignia. Soldiers are not authorized to wear pinned on badges in a field or deployed environment