http://defensetech.org/2010/07/20/u-s-south-korea-announce-invincible-spirit-exercises/#idc-container

Would The U.S. Just force the sub to surface? will the Sks shoot on sight?
What if its discovered inside strike range of a carrier?

Define ‘interfere’. If it surfaces near the group, no problem: past precedents are Chinese subs doing so. If it fires a torpedo, you bet ya it will be shot at if detected.