I think the heresy you are thinking of is docetism, which taught that Christ only seemed to be human; I believe certain forms of Gnosticism taught this also.
Although the line you quote could be taken that way if considered in isolation, I think that if you consider the following lines along with it, you get a different impression. In the version I learned, after "Veiled in flesh the Godhead see" comes:
"Hail the incarnate deity,
Pleased as man with men to dwell,
Jesus our Immanuel."
There is a clear indication that Jesus is God "incarnate", and that He is a man. So, whatever one may think of Christmas carols, or western hymns in general, I think we can absolve this particular carol of the docetist heresy.