"powerful presence" at this I laugh...
the United States contended with the Soviet Navy once upon a time, who did the same things.
They are probably going to send a small dispatch of ships or subs near US maritime borders stay in international waters. Then go home and chant about it and beat their chests. we might move the atlantic fleet out to say hello, the military has ways of detecting these things. aside from sonar, satalites, etc. not to mention now military planners are on alert for their naval movements.
on the bright side this might get the atlantic shipbuilders and sub docks some new contracts. god knows they need them.
it's kind of like a child who goes under the fence, comes back to brag to his friends "I'm so brave" though it would be funny he we did the military equilivent of spraying them with the hose, maybe send our air force to fly over the decks of any surface ships, or a few subs to contact them, hell have the CIA break their sub transmissions, not do anything but let them know they were hacked, that would be freaking helarious.
"this is Admeral Nuraki, of the Retribution, contacting high command."
"hello Admeral Nuraki, this is the USS Athena, how are things going down there?"
the look on his face would be priceless
or better yet... if the surface ships they send get hijacked or attacked by somli pirates, unlikely, but still funny.
in all seriousness, like I said, they'll come close and go home just to say "we got close to the "great satan" and lived we're awesome!" and we'll be watching them like a hawk the entire time, ready to send them to the deep should they take an agressive action.