In my experience, certainly with Fair Trading, it’s almost immediate. Fair Trading contacts the strata manager who then contacts the strata committee, all withing a matter of a couple of days, at most. I suspect it is an automated response.
As far as being dissuaded from proceeding when you tell the committee what you are planning to do, I think you have to give your SC a chance to comply or compromise with your wishes. If they don’t, then by all means gather your evidence and lodge a request for mediation.
But there are myriad reasons for committees not responding properly, ranging from indecision and lack of consensus to selective deafness; sometimes an application to FT is what it takes to get their attention.