You can use the discriminant analysis to predict the cluster using your principal components as independent variables, so your model would be:
And no, you don't have a restriction on the number of components you can use in regards to the number of clusters you have. I would use them all. By means of cross validation I would measure how well this model (linear discriminant) predicts the cluster and if the accuracy is good you would know that the clusters are separable, crisp, which could be interpreted as cluster health. Note that you could use any classifier to do this. You could also directly use separability measures for this same purpose like Jeffries-Matusita or divergence.