Are you only counting nuclear powered submarines? There are a lot more SSK's in NATO than that. They won't chase down a CVN BG, but if intelligence is good and planners are worth their beans, they can place a boat in the path of that BG. Just lay quiet like a hole in the water, let the leading escorts pass by and wait for the big prize. I'm not suggesting that a war between any NATO countries and the US is likely - although with the current US administration, the chances are low, but not zero.
I don't need Clancy's books - I was a submariner for twenty years and was a crewmember in a boat that penetrated a CVN screen. Today's modern torpedoes rarely miss their targets, so when the boat records a firing solution, that's considered a kill. To be clear, it's not all fun and games and Jolly Rodger flags. Opposing submarines are often detected and "prosecuted". And, no submarine captain is under the illusion that he is likely to escape after such an attack, as the series of ka-booms under that CVN hull will be a giveaway. The point is, no CVN BG commander would be so hubristic as to assume that any possible opposing submarines will be detected and eliminated before it can cause any harm.
