Yes, that's true, and they could theoretically span the world now. That said, it requires much more in the way of logistics--getting fuel to run those diesels. Plus, the need to run those diesels periodically makes the sub vulnerable and on the surface.
And while technically possible to go global, there's a much bigger impact on the crew, working on a D/E sub on such a basis. There are less "amenities" like fresh water available, perhaps video games and TV, eating conditions and the quality of food are less.
Nuke subs are “louder” because they can never completely shut down. Fuel cell systems allow of course to run a diesel underwater if needed for a recharge. They are vulnerable for fueling on resurfacing but they do not have to be stuck at ports for weeks at a time swapping nuke rods. Of course, in time of war that policy could change.