There's absolutely no way that that hypothesis may be correct. Dené-Caucasian is not just a highly disputed and far from consensually accepted macro-family in the field of linguistics, but it also necessarily dates to a very, very old time, because some of its constituent language families, which were already extremely divergent, are estimated to have started splitting themselves between 5000 and 6000 years ago - that is, even before the Yamnaya and Afanasievo cultures. Sino-Tibetan, with all its characteristics, was probably already spoken 6000 years ago, Dené-Yeniseian dates to at least 5000-6000 years ago, too. Dené-Caucasian, if it ever existed (I highly doubt so), was most definitely a Mesolithic or even Late Pleistocene language. This assumption assumes that the Dené-Caucasian language branches would be roughly as old as the particular branches of Indo-European, but that couldn't be further from the linguistic evidences, which point to an extremely higher linguistic divergence between the supposed Dené-Caucasian language subgroups compared to the Indo-European ones. Just to make it clearer, let's remember that while Afro-Asiatic is almost a consensus among linguists even though its constituent branches are extremely different from each other and its usual dating usually ranges from 10,000 to 20,000 years go, Dené-Caucasian is deemed as too tenuous to be accepted by most.
There's also the problem that Ukraine Neolithic and Eneolithic ancestry does not seem at all to be the main source of ancestry for the latter CWC, Bell Beaker, Sintashta and so on. More eastern (east of the Don river) sources in Khvalynsk and the Piedmont Steppe look much more plausible, and that in fact fits the archaeological evidences that point to a strong expansion of broadly Khvalynsk-derived culture (and presumably people) westward into Ukraine, changing Sredny Stog gradually into the more homogeneized cultural horizon of Yamnaya.
