I'm sure they'll have several coring runs into the hole as there...

I'm sure they'll have several coring runs into the hole as there is only so much core that can be cut and recovered to surface in a single run. I would think that MWD/LWD would be run only after all the core had been cut, and this would be potentially be the first opportunity to see the OWC if it's there (unless there's wireline on the rig as well?). I'm unsure how much information is gained from the core whilst it's still on the rig. The MWD/LWD would be able to log the cored section prior to drilling ahead and intersecting any lower targets as they drill to the final depth.