Can we combine multiple K-Means Models as a single model?
I agree with your assumption, the vector space is the same so I don't see any major problem with this approach.
Still this approach might cause some more subtle bias, depending on the differences between the models (sets of terms, number of clusters). I could imagine the following problems happening:

if there is a big difference in number of clusters between models, a model which has more clusters is more likely to contain the closest match, simply because it has more centroids. This might favour the most precise clusters (this might actually be a good thing, depends).
if there are many models sometimes there might be many close centroids across the models, and this would probably make the selection of the closest among them almost random: the exact position of a centroid is significant with respect to other centroids within the same model, not necessarily with respect to other centroids outside the model.