Yes it's extremely difficult not to leak (potential) information. This is called decoherence in these situations. It doesn't matter if you don't become consciou

Yes it's extremely difficult not to leak (potential) information. This is called decoherence in these situations. It doesn't matter if you don't become conscious of the measurement result as long as some atoms in your body gets contaminated by the measurement they get pulled into the same branch (or whatever concept you subscribe to, it all works the same).