I do believe it is possible to impulsively flirt without that being one's conscious intent. We are definitely capable of acting prior to understanding why we're doing what we're doing.
Please note that this is NOT the same as someone mistakenly believing someone else is flirting.
That's not flirting without meaning to. That's one person being mistaken about another person.
I originally wrote Grace directly asking Conan about this after clarifying that she was already in a relationship.
You may have already guessed that I decided I did not like that idea. Even if well-intentioned with Grace wanting to be clear she's not interested, that felt blunt, and like Grace would know that might hit like a hammer swing.
So I started thinking through how Grace would think this through, and, well...
Grace and me? Our trains of thought are prone to rampant track switching, and catastrophic derailment.