If a sub with a pirate targets a sub with a navigator, and the navigator changes course, does the pirate sub change course automatically to follow?

Yes, the Pirate will always aim for the shortest intercept course based on the sub's present conditions.

Of course, it's possible that they'll change course in a way such that the Pirate might not be able to reach its target in time. In that case, the Pirate will head for the sub directly and hope for the best (until it reaches its destination or changes course again).