Is it proper to say that clustering methods are mostly unsupervised learning techniques, with some exceptions such as model-based clustering?
Clustering is sub-class of unsupervised learning. Unsupervised learning techniques include clustering, feature extraction (e.g., PCA, Isomap, KODAMA), and feature selection (e.g., selection the variables with highest variance value). I think model-based clustering methods are still unsupervised techniques. Although you decide the model what you want, you do not use the information about the labels.