Here's the "official" response we received in email after the phone call to IHG CS: "As per your call regarding your Platinum status being a Chase Visa Card holder, I received an update from our Project Coordinator to please allow us 8 weeks from the first purchase to receive the upgrade to Platinum status."
My wife used the card yesterday for her HIX stay. So based on the information I just received, and the anecdotal information supplied by FT members, it looks like it will be 2...or 4....or 6....or maybe 8 weeks before she hits Platinum.