'twas my practice to monitor when using the NDB for tracking and absolutely so below MSA/LSA as appropriate. Otherwise one has no idea of its operational status.
I never found it distracting to have the audio turned down in the headphones to a level where I could hear it but it wasn't distracting. Of course, one needs CONSCIOUSLY to listen regularly/periodically, regardless of gain, to avoid the dits and dahs being pushed into the background hash. A few early I/F training exercises in the link where the instructor fails the aid - and the student continues on oblivious with the confidence of the needle sitting there like it was glued to the dial - usually is sufficient to get the message across.
Just a matter of practice, discipline and routine I would have thought .. like a lot of things in flying.