I am not sure why Song Confucianism would be put in opposition to Han Confucianism, it seems more reasonable to put to Song Confucianism in opposition to Ming Confucianism: Li-principle-based thought (Song) versus Xin-mind/heart-based thought (Ming) or also referred to as Zhu Xi school (Song) versus Wang Yangming school (Ming). So I first have reservations on the way the question is presented.
Not withstanding that, Qing officials would no doubt be more receptive to Song thought than to Ming thought just because of the reason that Qing had conquered the Ming dynasty, though we can't deny that Song thought might have prevailed on "merit" alone. As for Qing scholars finding that some Confucian texts that they thought were written earlier were in fact probably written much later which I think is what you are referring to as Han texts, remember that genealogy of Song Confucian text (and for that matter Ming texts) would not have been in much dispute by the Qing scholars, while Han texts since they were written nearly two millennia from Qing times, would obviously be a source of study and contention among the new kaozheng (validating authenticity) based scholars.
So, my answer would be a qualified answer: Yes, Qing preferred Song thought (but over Ming thought and not Han thought-not sure what Han thought would be considered as during that time) and kaozheng scholars would concentrate on authenticating Han texts just by default since Song and Ming era texts needed little authenticating. Remember that both Song and Ming thoughts were using Han texts and I would also note that some critical analysis of their correctness were being done by Song and Ming scholars even before Qing times though not in any sort of concerted way like the Qing scholars.