I think this might be looking at it in a rather skewed way, though I can understand where you're coming from. Firstly, "nations" and especially nation-states are a modern phenomenon -- the classic text on this is Benedict Anderson's Imagined Communities, though there's a very good recent study by Caspar Hirschi called The Origins of Nationalism which delves more into the medieval roots of the concept. The Holy Roman Empire shouldn't be considered a collection of nations on that account -- its constituent fiefdoms were not nations like, say, modern France or Germany.

Regarding the Holy Roman Empire itself, I think it's necessary to clear up a misconception on this. Often people will trot out Voltaire's witticism about the empire being neither holy nor Roman nor an empire and leave it at that, but serious scholarship of the Empire has to a large extent moved on from this perspective. The HRE, at least before the Thirty Years' War, was not fundamentally different from most other European kingdoms, which were also typically highly decentralised. It did end up differing in the degree of its eventual centralisation, but even when it was abolished by Napoleon it wasn't simply a figment of the political imagination. Joachim Whaley's very recent monumental two-volume study of the Holy Roman Empire (Germany and the Holy Roman Empire) does in my opinion an extremely good job of debunking some of the common conceptions about the empire simply being a political husk and so on.

So Germany wasn't in a completely peculiar situation in the way that you might assume. More immediately relevant to your question is the fact that the creation of a German national history happened to a large extent contemporaneously with other European nation-building projects. We shouldn't on that account expect too fundamental a difference between, say, the teaching of national history in France and in Germany. There are differences, of course, but these are to do with events that postdated this construction of a national history -- like the legacy of Nazism -- and not because of the Holy Roman Empire.

Onto the question itself: This will vary depending on the particular state you're talking about. As an example, though, the Bavarian state curriculum for secondary schools -- Bavaria being arguably the state with the strongest regional identity in Germany -- does cover specifically Bavarian history, but only in one part of one year and it's otherwise overwhelmingly concerned with European and German history as a whole (see page 53 here (pdf) for an overview in German). This is already more regional history than you'd find in, say, the British history curriculum -- at least in my own experience of it -- but it certainly doesn't qualify it as a regionally focused curriculum in the way you're suggesting. Moreover, this regional focus, to the extent that it exists, is to a large degree an effect of the federalism that has come to dominate in Germany since the Second World War, rather than simply a consequence of historically deep-seated regionalist fragmentation.

The overall point: regional history is taught in Germany, perhaps to a greater extent than in many other countries, but you shouldn't consider this to be a legacy of the Holy Roman Empire.