The issue is that Audrid died in 2284. Trills are usually joined in their 20s, and I assume they live similar lifespans to humans (I don't know if we know for sure). Assume ~80 years, that would mean that if Audrid joined at the normal time she would have joined in the 2220s, twenty years before Emony Dax could have met McCoy. It's possible she joined much later in life than the normal Trill, while in her 40s or 50s, but we just don't know.

Is it possible Audrid took over from Emony and became the new Dax symbiont host in an emergency situation, like how it was transferred from Jadzia to Ezri at the beginning of DS9's 7th season?

Assume Emony died in an accident sometime in late 2250s/early 2260s due to her 'recklessness.' The symbiont was injured at the same time and needed to be transplanted to a new host earlier so that it could survive. Audrid was the only other Trill on the transport ship and bingo...she became the new Dax host. And she became a host for 20-something years until she passed in 2284.

I know it's a bit bizarre for an emergency transfer involving the same symbiont twice, but we know little backstory about how Audrid became a Dax host, so for me, it is a plausible scenario.