Yes.
However, there is generally no reason to do this. The reason is that most applications understand a particular XML LANGUAGE, such as one used to TRANSFER sales orders between companies. If the element type and attribute names in the language belong to an XML namespace, the application must be namespace-aware; if not, the application must be namespace-unaware.

For a few applications, being both namespace-aware and namespace-unaware makes sense. For example, a parser might choose to redefine VALIDITY in terms of universal names and have both namespace-aware and namespace-unaware validation modes. However, such applications are uncommon.

Yes.
However, there is generally no reason to do this. The reason is that most applications understand a particular XML language, such as one used to transfer sales orders between companies. If the element type and attribute names in the language belong to an XML namespace, the application must be namespace-aware; if not, the application must be namespace-unaware.

For a few applications, being both namespace-aware and namespace-unaware makes sense. For example, a parser might choose to redefine validity in terms of universal names and have both namespace-aware and namespace-unaware validation modes. However, such applications are uncommon.