No, it's not why you said "might".
You said 'if you've got an extractor'.
If you knew what you meant, you'd say 'if you have an extractor operated by a switched live from the light switch'.
RCD's don't detect flames or sparks or smoke.
RCD's are there to detect any leakage of current to earth, which if there isn't, won't trip, so it sounds as though there wasn't any sufficient earth leakage.
The JCC fire guard fittings are very good.
Peoples views on fitting fire rated fittings are mixed.
I would go fire rated because if you don't, the ceiling is now worse than it were before even if it wasn't documented as being fire rated, it will have offered some protection.
Plus the...