Inertial Navigation Systems are good pieces of hardware, and without giving anything away I can tell you that you can assume most major warships in any of the better NATO navies will be equipped with it. However, no unit (surface or submarine) relies on it as a principal means of navigation, certainly not for months at a time. It is a system that starts out accurate and gets progressively less and less so as you go, especially in rough seas. Remember, it has to add up every bit of inertia in every direction - including wave motion. By the time you reach your destination your area of probability can be so large that celestial navigation (using modern instruments) can actually be more accurate. INS has to be periodically corrected, and when GPS isn't available or is degraded (or we are training without it), this is done by old fashioned traditional navigation methods. Fixes based on visible features (land, nav markers), celestial fixes, bottom contour fixes, etc. It's bottom contour fixes using depth sounders that submerged vessels use as their primary means of navigation.
INS does have its uses. And while I can't discuss when and what situations would call for its use as a primary means of position fixing, it probably shouldn't be too hard to work out likely scenarios. Traditional navigation is still king. INS is only used as a primary means of navigation by the authors of war novels.