Can I apply Clustering algorithms to the result of Manifold Visualization Methods? Some methods related to manifold-learning are commonly stated as good-for-visualization, such as T-SNE and self-organizing-maps (SOM).

I understand that when referring specifically to "visualization" means that the non-linear dimensionality reduction can provide good insights of data in its low-dimensional projection, but that most commonly this low-dimensional projection cannot be used in machine learning algorithms, since some of information of the high-dimensional structure is lost (roughly).

However, and here the question, If "clusters" are being observed in the visualization is it acceptable to apply a clustering algorithm to the low-dimensional transformed data and analyze the clusters or groups separately?

For example, I'm applying T-SNE to rather-high dimensional data (40 features) and obtaining this representation:



Disregarding the colors you observe in the picture, I would like to apply a clustering algorithm and separate the data from the found clusters (let's say 6 or 7 clusters), and then analyze the characteristics of each cluster using the high-dimensional representation of each point.

This is in synthesis: using the low dimensional to find clusters, and analyze (exploration) each cluster separately using the high dimensional representation. If I'm not able to do this, I don't see the actual point of visualizing in the low-dimensional space, in a practical sense.

I understand T-SNE preserves well local structures and less accurately global structures, is this a drawback to do why I want? Is this low-dim clustering approach more suitable for other manifold learning methods?

EDIT:
Probably a more direct way of asking this is: Can I use observed clusters in low dimensional representation to label or tag examples, and use these labels for discrimination using the original high dimensional representation?
You can do anything you want in the low dimensional space, and can try to validate as well. By clustering the above, you are in effect assigning features/tags to your data points in higher dimensions. Remember, tSNE tries to preserve distances, so that points in high dimensions will remain close to each other in low dimensions. 

With that in mind, don't forget that no two instances of tSNE will be the same, which means that your clustering centers will be different each time you run tSNE.