The answer is yes! Both session state provider can be setup to use the same connectionstring name.

But note this is not recommended due to performance concerns.

In database(SQL), they are distinguished by Application names as below:

And while looking at these, made a few other connections as well.
  • Asp.Net SessionId -> Private session key
  • Sitecore Analytics Global Cookie -> Shared session key -> Contact GUID in MongoDB -> Contact ID