words - ברוך שם כבוד מלכותו לעולם ועד after a bracha with a false statement

If we make a bracha levatala or say Hashem's name by accident, we say ברוך שם כבוד מלכותו לעולם ועד.

Is this true only if the original bracha is a valid praise of Hashem, or even if it contains false statements? For example:

• Sefardi women saying a bracha on an mitzva that applies only to men (וצונו is false according to Sefardim)
  
  
  
  • or I guess similarly, a Sefardi Kohen or Levi saying the bracha on pidyon haben
  
  
  
  
  


• for everyone, a zar saying the bracha on birkat kohanim (אשר קדשנו בקדושתו של אהרן is definitely false, for Sefardim וצונו is also)


• any bracha that contains יום ____ הזה on the wrong day

Is the function of ברוך שם to turn the bracha that you already said into a praise, which might not work in this case because your praise is false? Or is it a standalone praise of Hashem because you mentioned His name, and the context wouldn't matter?