Can we combine multiple K-Means Models as a single model? I have a NLP problem statement where I use a Word2Vec embedding pre-trained model to convert key text to vectors and then on a set of terms run k-means clustering to get a final model for certain k
For various sets of terms, I would develop a different model, which I would store to disk.
My question is, in case there is a new term, which I wish to classify as to which cluster should it point to from all the models can I follow the following approach?

Load all models to memory and get their cluster centers.
get the vector of the new term based on the same pre-trained model as before.
get distance from each cluster center to the new vector and whichever is nearest can be considered as the winning cluster

I would like to know what could be the possible drawbacks of such an approach.
My assumption is that since the vector space is same as defined by the pre-trained model, therefore the cluster centers would be in the same space.
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.