Sorry, but those two are contradictory.
First you express a thought that asking conjugation questions is how native speakers proccess cases. So there is some use in those questions to foreigners as they help them think as we do when composing Russian sentences.
Then, you state that you don't know how our brain proccess cases.
As to why I asked if you use conjugation questions when speaking Russian. Well, that's entirely because of your question that is quoted in this message. To be more specific, the first quote.