The way I see this.
1) No, shields do not subtract armor rating. I think this is known issue (before patch) with some talents that improve armor rating to only do that to back armor, and not front armor stat, resulting in lower frontal armor for all warriors (not just shield warriors)
2) Crafted shields before patch have armor rating of zero. Removing such shield adds 5 points to frontal armor since default shield has front armor of 5. If you equip two-handler, you'll lose those 5 points.
3) Crafted shields after patch as well as bought shields correcly add to front armor rating. If back armor is shown as higher, this is due to issue 1
This was all tested in exploration area (not Heaven/Skyhold), when specific companion is slected before going to attributes section.