From the wording of your question, I'm not sure what you're after. Eric Hobsbawm and Terrance Ranger, The Invention of Tradition (Cambridge: Cambridge University Press, 1983)described how some national traditions were invented. That is not to be mean that it was always (or even typically) a callus, purely-contrived process. Rather, It seems to me that Hobsbawm was speaking about how traditions could well up, seemingly out of nowhere, and that they didn't necessarily have deep roots. That is not to say that no traditions have deep roots.

Folklorists and ethnographers understand that culture is a dynamic thing and that it constantly changes. In addition, culture can be conservative, resisting change and yielding to transformations only slowly. In a sense, all traditions are new, in the sense that if one goes far enough into the past, the counterpart of that "tradition" will look very different from what is practiced today. At the same time, some traditions can link back to past practices. Others can be more recent "inventions."

All this said, I'm not sure what you're after, so clarification may get you the answer you seek.

So, I understood your question a little differently than the previous answer, and since it’s one that I really enjoy discussing with my students I’m going to jump in, even though I agree with the other answer. As I read it, what you are asking is whether, if we accept that Hobsbawm was right and national traditions are constructed, can we ever regard any tradition, national or otherwise, to not have been constructed?

My answer, at least, would be no. What’s important to acknowledge, though, is that ‘constructed’ is not the same thing as ‘fake’, or in another way, just because something is constructed doesn’t mean it isn’t real (as I point out to my students: buildings are constructed – if they weren’t real, this class would be a lot more damp (I teach in Scotland)). What Hobsbawm is warning against is the assumption that certain aspects of our culture is natural, inevitable and everlasting. While many of our traditions may indeed be a reaction to the natural world, these reactions are still filtered through our own understandings and perceptions – in other words, how we react to nature is cultural. That doesn’t mean these traditions lack meaning, or aren’t old or aren’t basically a good thing, but rather that they aren’t immutable and we shouldn’t assume that they were always there and always will be.

There’s a reason that Hobsbawm and others are particularly concerned with nationalism when they put these arguments forward. Nationalism is one of the most influential political ideas of the past couple of centuries or so, and represents a very successful effort to ascribe meaning to something beyond our day to day existence – an imagined community, as Benedict Anderson would put it. What is so striking about national identity is just how deliberately it was constructed across so many contexts – the product of artists, writers and politicians striving to add depth and meaning to a national concept. History, and historians, were a key part of this – finding historical evidence that this imagined nation had a factual, historical basis. That the nation was natural, everlasting and immutable, in other words.

So, when Hobsbawm casts doubt on this process, he is in many ways confronting the original sin of the history profession – the willing participation in a process designed to cement the power and legitimacy of the nation. That doesn’t mean that national identities aren’t real or don’t have consequences (as anyone who ever wandered into the wrong bar during a football game can attest), but rather that they aren’t and shouldn’t be seen as natural or inevitable. The job of the historian, as Hobsbawm and others came to realise, should be to question these claims to arrive at a better understanding of the past, not to slavishly participate in their construction and maintenance.