No. The cap covers the threads only a small portion lines up with the crown. The cap is more of a thread protector then an actual cap.
+1. The cap simply covers the threads on the outside. The crown is independent of the thread protector.
You could also add a muzzle brake, since it's already threaded. I don't like shooting my 300 WM suppressed. The suppressor has too much of a large push and pulls me off target during recoil. A good muzzle brake works much better for recoil recovery. I can spot my hits from about 200 yards and out with my braked 300 WM. I'd struggle to see my hits from 400-500 yards or closer shooting suppressed.