When you say ArcSDE 10.1, are you saying that you geodatabase is at the 10.1 release or that you are running the ArcSDE 10.1 application service or both? In other words, I just want to verify that your GDB itself has been created at or upgraded to the 10.1 release that matches the desktop client.
In terms of the first error, I've researched the HRESULT code and it does not appear to be documented online from Esri. You may need tech support to help troubleshoot this issue. Have you been able to create, import, and modify metadata for tables and feature classes without issue using the same user account?
In terms of the second error, I've seen this quite a bit in ArcCatalog when selecting the Description tab. I don't know if it's necessarily a symptom of or related to the first error you're seeing, though. I've seen this occur for views (and sometimes for feature classes and tables) if there is no well-formatted XML present for that object class. Once metadata is able to be added, that error disappears usually.
To answer your question, I believe the answer I can give you is 'yes' based solely on my opinion. I was able to import metadata from a table to a view using the Metadata Importer tool without getting the first error. I also can't find any information online that states that views registered with the geodatabase don't support database so I can only assume they do especially since I don't get the error you are seeing.
I did find some older, Esri-documented rules for metadata for spatial views, which are similar to regular views:
(1) The spatial view must contain an Object Id column; (2) The spatial view must be registered with the geodatabase; (3) Metadata can only exist for items registered with the geodatabase; and (4) Only the owner of a spatial view can edit the metadata for that spatial view.
I think in your case, I think you probably have 1 - 3 covered already but I am not certain about #4. Does the user account you're using to connect to SQL Server via ArcCatalog and ArcToolbox have admin rights (or assigned db_owner role, for example) on the database?