Peter,
Give them a call before leaving the airport. It certainly can't hurt.
I'm not 100% sure but they probably can tell you. We stayed at the VWL for 2 nights and then OKW for 2 nights in March. I called OKW in the morning of our check-out/check-in day to see if our room was ready. They told me to come right over because they had (I think) "rack" rooms ready even if "our" room wasn't yet. So, we lugged our stuff out to the car and drove ourselves over and checked-in before heading to the parks. I felt "home" even before entering the unit. Just parking in front of the unit got me relaxed. No need to get EVERYTHING out of the car in 2 minutes before the valet took it away!
If OKW isn't fully booked, they could probably give you a room already clean and empty. Unless, you have specific requests that were actually granted that you want to keep.
What's the worst that can happen? They'll tell you that they can't tell you so you head on over to wait anyways?
If you don't want to grocery shop before your unit is ready and you are settled in and you are in limbo waiting for your room, park at HH, check on the approximate time that the room is ready,, and hop on the ferry to DTD if there's time.
We love OKW! Although, we're looking forward to staying at BWV & BCV in a few weeks, I find myself a little disappointed that I won't be going "home" to OKW. I really need a relaxing vacation right about now! Hey, anywhere in Disney is better than home.
Have a great trip!