Since hextech crystals are often containers of Brackern-souls or fragments of it...
... wouldn't it theoretically possible to communicate with them? Sure, you would either need a strong telepath or a technological bridge that fulfils that function, but it shouldn't be impossible.
The only question is what the crystal had to say... if they even remember their past experiences or if they have completly changed into the form of the tool they are used in now. Like, let's take the crystal that powers the hammer of Jayce: would it be like "WHAT HAVE YOU DONE TO ME, MORTAL?!" or more like "Yo I'm your badass hammer, finally I get to talk to you. Btw, you're kind of a douche sometimes. Also, I demand a proper politure and repairs every single evening, or I refuse to function for you!"
Having sentinent weapons is not exactly anything new, the concept exists and the Darkin are living proof of it. Could Jayce's hammer be theoretically a proto-darkin then? Imagine if the sentinence inside the crystal would actually develop through interaction (as opposed to now where it seems to be in isolated coma), and it was actually able to influence its users?
Or wait, maybe that's already happening and the radiation from his hammer is already changing Jayce's mind in a way we don't know yet?
The implications of all this might reach further than we had thought...