I think it is fair. If Kid thought Conan was just a real little boy, he'd always be subconsciously underestimating him, probably. There is the fact that Kaito thinks sideways to be dealt with, but still. That very fact would lead him to wonder why the little kid just happens to be one of his best critics. Whereas on the other hand if Conan knew then the info would be at odds with his detective's sense of justice - he'd probably want to just have things as before (heists are fun and harmless), but not be able to throw the info away, and so have to do something with it.
On the 'Is it possible?' part of the thread, I'd say yes. Going from sources, the Kid would know that Conan reacts to the 'method acting' psyche like an adult, doesn't react around a body the same way normal children would, etc. etc. That's not even mentioning the HOW of how he found out in the third movie, which hadn't really been brought up!